Graph Operations
M-polynomial of some graph operations and Cycle related graphs
... In this paper, we have proposed new operators to derive general sum connectivity index and first general Zagreb index of a graph from the respective M-polynomial. Further, we have obtained M-polynomials of some ...
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Wiener Index of a Cycle in the Context of Some Graph Operations
... molecular graph provides a rough measure of the compactness of the underlying ...connected graph G is the sum of the distances between all pairs (ordered) of vertices of ...
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The Hyper-Zagreb Index of Graph Operations
... Let us begin with a few examples, then we will give a crucial lemma related to distance properties of some graph operations. Our main results are applications of this lemma in computing exact formulae for ...
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Product Cordial Graph in the Context of Some Graph Operations on Gear Graph
... some graph elements in gear ...gear graph. Similar problems can be discussed for the graph obtained by duplication of an edge in gear ...these graph operations of wheel graph, ...
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Some New Results On the Hosoya Polynomial of Graph Operations
... a graph invariant that has found extensive application in ...a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiener ...on graph ...
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A Note on Revised Szeged Index of Graph Operations
... the revised Szeged index of the Cartesian product of two connected graphs. In this paper we compute the revised Szeged index of the join and corona product of graphs. Readers interested in more information on computing ...
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On exponential domination and graph operations
... set. Graph operations are important methods for constructing new graphs, and they play key roles in the design and analysis of ...of graph operations including edge corona, neighborhood corona ...
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Computing bounds for the general sum-connectivity index of some graph operations
... several graph operations. These operations include corona product, cartesian product, strong product, composition, join, disjunction and symmetric difference of ...
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On the Harary index of graph operations
... The paper is organized as follows. In Section , we obtain lower and upper bounds on the Harary index of graphs. In Section , we give some exact expressions for the Harary index of various graph ...
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Spectra of Some New Graph Operations and Some New Class of Integral Graphs
... In literature, many graph operations such as disjoint union, NEPS, corona, edge corona, neighborhood corona, common neighborhood graphs, etc., have been introduced and their spectral properties have been ...
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Modified Generalized Degree Distance of Some Graph Operations
... various graph operations containing Cartesian product, composi- tion, join, disjunction and symmetric difference of graphs, whose concepts will be presented in later ...some graph operations. ...
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Sharp Upper Bounds for Multiplicative Degree Distance of Graph Operations
... A topological index of a graph is a numerical quantity which is structural invariant, i.e. it is fixed under graph automorphism. The simplest topological indices are the number of vertices and edges of a ...
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Applications of Graph Operations
... A graph G with a specified vertex subset U V(G) is denoted by ...the graph with vertex set V(G) V(H) and two vertices (g, h) and (g′, h′) are adjacent if and only if g = g′ U and hh′ E(H) or, gg′ ...
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On two energy like invariants of line graphs and related graph operations
... In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve ...
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Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
... A graph G with a specified vertex subset U V(G) is denoted by ...the graph with vertex set V(G) V(H) and two vertices (g, h) and (g′, h′) are adjacent if and only if g = g′ U and hh′ E(H) or, gg′ ...
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The Generalized Wiener Polarity Index of some Graph Operations
... Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the ...
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On Powers of Some Graph Operations
... In this section, we compute the Wiener index and the Wiener polarity index of G4 H and G 5 H . The Wiener index [11] defined as the sum of distances between all vertex pairs in a connected graph. While the Wiener ...
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The multiplicative Zagreb indices of graph operations
... These two graph invariants are called multiplicative Zagreb indices by Gutman (Bull. Soc. Math. Banja Luka 18:17-23, 2011). In this paper the upper bounds on the multiplicative Zagreb indices of the join, ...
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The Generalization of Graph Operations and Their Local Metric Dimension
... Let 𝐺 be a connected graph with vertex set V(G) and 𝑊 = {𝑤 1 , 𝑤 2 , … , 𝑤 𝑚 } ⊂ 𝑉(𝐺). The representation of a vertex 𝑣 ∈ 𝑉(𝐺) with respect to 𝑊 is the ordered m-tuple 𝑟(𝑣|𝑊) = (𝑑 𝑣, 𝑤 1 , 𝑑 𝑣, 𝑤 2 , . . . , 𝑑 𝑣, ...
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Computing GA4 Index of Some Graph Operations
... a graph means a collection of points and lines connecting a subset of ...a graph also called vertices and edges of the graph, ...connected graph is a graph such that there is a path ...
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