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Vertex weighted Laplacian graph energy and other topological indices

Vertex weighted Laplacian graph energy and other topological indices

n . In this paper, we consider several natural vertex weights of G and obtain some inequalities between the ordinary and Laplacian energies of G with correspond- ing vertex weights. Finally, we apply our results to the molecular graph of toroidal fullerenes (or achiral polyhex nanotorus).

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On the Non Common Neighbourhood Energy of Graphs

On the Non Common Neighbourhood Energy of Graphs

Abstract In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ENCN G , NCN-energy for some standard graphs is obtained and an upper bound fo[r]

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On Eccentricity Version of Laplacian Energy of a Graph

On Eccentricity Version of Laplacian Energy of a Graph

A large number of results on the graph energy have been reported, see for instance [2, 8, 10, 13]. Motivated by the success of the theory of graph energy, other different energy like quantities have been proposed and studied by different researchers. Let D(G) = [d ij ] be the diagonal matrix associated with the graph G, where

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Laplacian Sum-Eccentricity Energy of a Graph

Laplacian Sum-Eccentricity Energy of a Graph

[25] Y. Z. Song, P. Arbelaez, P. Hall, C. Li, A. Balikai, Finding semantic struc- tures in image hierarchies using Laplacian graph energy, in: K. Daniilidis, P. Maragos, N. Paragios (Eds.), Computer Vision – CECV 2010 (European Conference on Computer Vision, 2010), Part IV , Springer, Berlin, 2010, pp. 694–707.

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Milovanovi’{c} bounds for minimum dominating energy of a graph

Milovanovi’{c} bounds for minimum dominating energy of a graph

For details on the mathematical aspects of theory of graph energy see the papers [4, 5] and the references cited there in. The basic properties including various upper and lower bounds for energy of a graph have been established in [7, 8] and it has found remarkable chemical applications in the molecular orbital theory of conjugated molecules [2, 6].

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Improved McClelland and Koolen–Moulton bounds for distance energy of a graph

Improved McClelland and Koolen–Moulton bounds for distance energy of a graph

its adjacency matrix. The studies on the graph energy can be seen in papers [5, 6]. For a de- tailed survey on applications to the graph energy, see [2–4, 7]. For the ordinary energy, the best known bounds are the Koolen and Moulton upper bound [9, 10] and the McClelland lower bound [12].

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Minimum Covering Randić Energy of a Graph

Minimum Covering Randić Energy of a Graph

Theories on the mathematical concepts of graph energy can be seen in the reviews[3], papers [4] [5] [6] and the references cited there in. For various upper and lower bounds for energy of a graph can be found in papers[7] [8] and it was observed that graph energy has chemical applications in the molecular orbital theory of conjugated mo- How to cite this paper: Kanna, M.R.R. and

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Vol 11, No 8 (2020)

Vol 11, No 8 (2020)

J. Liu and B. Liu defined the Seidel energy graph in generalization for Laplacian energy and analyze. For the Seidel energy bound using the rank of the sediel matrix and extended the concept of energy to Hermite matrix. Willem H. Harmers in Seidel switching and graph energy investigates that Seidel switching changes the spectrum, but not the energy and present an infinite family of example with maximal energy. In this chapter the seidel matrix [15] which is the generalization of the adjacency matrix is analyzed for sharp bound of the Seidel energy for the connected and disconnected graph. In this paper we find few bounds which relate domination number of book graph , and Seidel energy of book graph and rank of the incident matrix of the book graph and pose some open problems for further research. The motivation for this paper is to establish a link between there parameters. This is the chapter motivated from the Paper [1]. CLEMENTS BRAND, NORBERT SEITER, Eigen values and determination in graph, Mathematic Slovaca, Vol.46 (1996). No. 1.1,33 – 39, where the authors had found the relation between largest eigen value of the Laplacian matrix and Domination number.
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2 -quantum  Info.doc

2 -quantum Info.doc

Finally you've got to steer the beam so it smashes into something. The two smashing methods are fixed target and colliding beams. For fixed target, you slam a beam of particles into some stationary chunk of matter. The advantages of the fixed target method are: (a) it's easier to aim the beam at a large non-moving target, (b) lots and lots of protons are available in chunks of matter, and (c) most all the products of the particle interaction will be moving in a very definite forward direction, so you can easily build detectors in the forward region to detect them. The disadvantages are that chunks of matter pretty much only provide protons and neutrons to smash into--the electrons aren't concentrated enough to be consequential--and there are certainly no anti-protons or positrons (anti-electrons). Also, a target which is just sitting there does not bring any kinetic energy into the equation. Since you are typically trying to convert energy into massive particles (via E = mc 2 ), more energy is better.
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Energy Efficient and Improved Certificate Revocation Technique for Mobile Ad Hoc Networks

Energy Efficient and Improved Certificate Revocation Technique for Mobile Ad Hoc Networks

In the nonvoting based process a node with a valid certificate selects a node as a malicious aggressor to revoke its certificate. J. clulow et al [9] planned the suburbanized suicide-based approach “suicide for the good strategy, certificate is revoked through only 1 accusation. This will at constant time revokes certificates of every accused node associated exculpatory node to urge obviate AN aggressor from the network; the exculpatory node has to sacrifice itself. Even though the process gradually reduces the time necessary to eject a node as well as communication overhead, but this suicidal approach doesn't take into thought to differentiate falsely suspect nodes from real malicious attackers. Park et al. [10] planned a cluster based certificate revocation theme; where nodes endure self-organized in the direction of create clusters. A positive certification authority do liable in the direction of hold the individual and suspect node at intervals the warning list (WL), blacklist (BL) and manages management messages correspondingly. And in addition it deals with the matter of false accusation the malicious aggressor node certificate is revoked by any solitary neighbouring node. Thus takes short time to complete certificate revocation methodology. [12]In this paper, author given associate in nursing energy-efficient distributed clump process for ad-hoc networks. The approach is hybrid: cluster heads area unit haphazardly hand-picked supported their on the market energy and nodes connect with clusters specified communication price is decreased. During this paper, author proposes a replacement energy economical approach for clump nodes in unintentional device networks. Author presents a protocol, HEED that sporadically selects cluster heads per a hybrid of their residual energy and node proximity towards its neighbours or node degree to boost network life
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A Study on the Impact of Ethical Behaviour of Firms on Global Competitiveness Ranking

A Study on the Impact of Ethical Behaviour of Firms on Global Competitiveness Ranking

Let G be a graph, 𝑥𝑥 𝑖𝑖 (𝐺𝐺) be the number of vertices of degree 𝑖𝑖, 𝑥𝑥(𝐺𝐺) be the order of G, and 𝑦𝑦 𝑖𝑖𝑖𝑖 (𝐺𝐺) be the number of edges that link vertices of degree i and j. A chemical graph is a graph in that no vertex has degree greater than 4. A common linked graph with x vertices and x + 1 edges is called a bicyclic graph. Assume that 𝑣𝑣 1 is a vertex of 𝑇𝑇 𝑒𝑒 and 𝑣𝑣 𝑝𝑝 is a vertex of 𝑇𝑇 𝑟𝑟 . Combing 𝑣𝑣 1 and 𝑣𝑣 𝑝𝑝 by a path 𝑣𝑣 1 , 𝑣𝑣 2,,,,,, 𝑣𝑣 𝑝𝑝 of length p−1, where p ≥ 1 (p = 1 means determine 𝑣𝑣 1 with 𝑣𝑣 𝑝𝑝 ), the answering graph, described by D(e, p, r) described in Figure 1, is called an ∞-graph. Let 𝑃𝑃 𝑒𝑒 +1 , 𝑃𝑃 𝑝𝑝+1 𝑎𝑎𝑎𝑎𝑑𝑑 𝑃𝑃 𝑟𝑟+1
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Randi ́c Energy and Randi ́c Estrada Index of a Graph

Randi ́c Energy and Randi ́c Estrada Index of a Graph

In this paper, the Randi´c Estrada index of a graph is introduced. Also the Randi´c energy and the Randi´c Estrada index are studied. In section 2, a sharper upper bound and a new lower bound for the Randi´c energy are obtained. In section 3, some bounds for the Randi´c Estrada index involving Randi´c index, Randi´c energy and some other graph invariants are also put forward.

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Energy of Fuzzy Labeling Graph [EFl(G)]- Part II

Energy of Fuzzy Labeling Graph [EFl(G)]- Part II

Let the graph G(V;E) where V be vertices and E edge. Graph theory involves lot of applications such as geometry, algebra, number theory, topology, operations research, and optimization and computer science. In 1967, most graph labeling methods trace their origin introduced by Rosa [11] and Graham and Sloane [5] introduced harmonious graceful graph by additive bases in 1980. Gallery proof of lebeling results given by Gallian[6] in aDynamic Survey of Graph Labeling. Pradhan and Kumar [10] proved that graphs obtained by adding a pendent vertex of hair cycle ʘ are graceful if n≡0(mod4m).They further provide a rule for determining the missing numbers in the graceful labeling of ʘ and of the graph obtained by adding pendent edges to each pendent vertex of ʘ . Abhyanker[2] proved that the graph obtained by deleting the branch of length 1 from an olive tree with 2n branches and identifying the root of the edge deleted tree with a vertex of a cycle of the form is graceful. In 1985 Koh and Yap[8] generalized this by defining a cycle with a -chord to be a cycle with the path joining two nonconsecutive vertices of the cycle.
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Theoretical Study of Thermodynamic and Quantum Energy on Carbon Nanotubes Armchair (5,5) and its Derivatives

Theoretical Study of Thermodynamic and Quantum Energy on Carbon Nanotubes Armchair (5,5) and its Derivatives

The increasing number of phosphorus atoms in the nanotubes relative increase in absolute total energy is the electron energy. Other results of this study was to obtain structural relationship with the electron energy using the QSAR And electron energy levels for the four other nanotubes were predicted on the basis of this method.

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Energy of Complete Fuzzy Labeling Graph through Fuzzy Complete Matching

Energy of Complete Fuzzy Labeling Graph through Fuzzy Complete Matching

In 1965 Fuzzy relations on a set was first defined by Zadeh [14].The nature of values discussed in energy of graph is never an odd integer [3] and energy of a graph is never the square root of an odd integer [13].Study on energy of different graphs such as regular, non-regular, circulate and random graphs [4, 5, 6] by I.Gutman and shao.In [1] Anjali Narayanan and Sunil Mathew introduced the concept of the energy of fuzzy graph.

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Comparing energy and Randic energy

Comparing energy and Randic energy

4. AGREEMENTS BETWEEN E AND RE Within various classes of molecular graphs, a reasonably good (increasing) linear correlation between Randić energy and total π-electron energy could be established. As characteristic examples, we present here such correlations for chemical trees (Figure 1) and catacondensed benzenoid hydrocarbons (Figure 2). From Figures 1 and 2 (as well as from the analogous computational results not presented here), we conclude that the main structural factors that influence the total π-electron energy also influence (in the same sense) the Randić energy. Recall that in the case of chemical trees, .
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A graph-based signal processing approach for low-rate energy disaggregation

A graph-based signal processing approach for low-rate energy disaggregation

Inspired by the initial success of GSP in many fields [15], [16], [17], in this paper, we propose a GSP-based NALM ap- proach by extending [17] to perform low-complexity multiclass classification of the acquired active power readings without the need for event detection to detect appliance changing states, e.g., switching on/off. We index the acquired power signal by a directed graph where each vertex corresponds to a load sample and the weights of the edges connecting the vertices reflect the degree of similarity between the nodes. Then, we define an optimization problem that contains as the regularization term the total graph variation, that is, we apply regularization on the constructed graph signal to find a signal with minimum variation. Our experimental results using publicly available REDD dataset [18] demonstrate high potentials of the proposed approach.
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Reciprocal Graphs

Reciprocal Graphs

In this paper, we construct some new classes of reciprocal graphs and an upperbound for their energy is obtained. Pairs of equienergetic reciprocal graphs on n ≡ 0 mod ( 12 ) and n ≡ 0 mod ( 16 ) are constructed. The Wiener indices of some classes of reciprocal graphs are also obtained. These results are not found so far in literature.

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Computing the energy of small fullerenes

Computing the energy of small fullerenes

This graph invariant is very closely related to a chemical quantity known as the total π-electron energy of conjugated hydrocarbon molecules, see [1,2,4,5].. The energy of all isome[r]

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Performance Enhancement of Domestic Refrigerator Using Hydrocarbon Mixture R 436A as Refrigerant

Performance Enhancement of Domestic Refrigerator Using Hydrocarbon Mixture R 436A as Refrigerant

From Graph 1, it is observed that pull-down time of domestic refrigerator by using refrigerant R-436a is higher as compared to that of refrigerant R-134a by about 25%. From Graph 5, it is observed that energy consumed for pull-down period of domestic refrigerator by using refrigerant R-436a is lower as compared to that of refrigerant R-134a by about 23.6% which is reflected by better COP.

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