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On marker set distance Laplacian eigenvalues in graphs.
... on eigenvalues and eigenvector components of weighted adjacency ...the Laplacian matrix and its associated vector components yield the clustering of vertices in the ...and distance matrix of a graph ... See full document
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Bounds on normalized Laplacian eigenvalues of graphs
... A set of vertices X of G is called a cover of G if every edge of G is incident to some vertex in ...vertex set X is a vertex cover if and only if X is an independent ... See full document
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Eigenvalues of the resistance distance matrix of complete multipartite graphs
... simple graphs, that is, graphs without loops and ...vertex set V = { , , . . . , n } and an edge set E = ...resistance distance [] between any two vertices i and j, denoted by r ij , ... See full document
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On Laplacian and Normalized Laplacian of a Social Network
... a set V of vertices and a prescribed set E of unordered pairs of ...Graph eigenvalues have prominent connections with several areas of ...expander graphs and their eigenvalues are ... See full document
7
Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues
... The numbers of its vertices and edges are denoted by n(G) and m(G) (or n and m for short). For a vertex v ∈ V (G), let N(v) be the set of all neighbors of v in G. The degree of v, denoted by d(v), is the ... See full document
17
On the sum of the two largest Laplacian eigenvalues of unicyclic graphs
... vertex set V (G) and edge set ...the set of all neighbors of v in G and let d(v) = | N(v) | be the degree of ...maximum distance among all pairs of vertices in ... See full document
8
Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph
... two AutoGraphiX (a software package devoted to conjecture-making in graph theory) conjectures on remoteness, vertex connectivity and algebraic connectivity. Sedlar [7] also studied AutoGraphiX conjectures involving ... See full document
12
Energy of graphs
... graph eigenvalues, namely the sum of the eigenvalues of the adjacency matrix A ( G ) of ...the Laplacian energy of a graph as the sum of the absolute deviations of the eigenvalues of its ... See full document
6
On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs
... the eigenvalues of the complementary distance signless Laplacian matrix of graphs obtained by some graph ...complementary distance signless Laplacian energy of ... See full document
21
Properties of characteristic polynomial of marker set distance and its Laplacian
... connected graphs G 1 and G 2 are said to be marker set distance isomorphic if there exist marker sets M 1 of G 1 and M 2 of G 2 such that DDS M 1 (G) = DDS M 2 ...two marker ... See full document
12
A new localization set for generalized eigenvalues
... So, in this case, (A, B) has n generalized eigenvalues. Moreover, if B is singular, then the degree of the characteristic polynomial det(A – λB) is d < n, so the number of general- ized eigenvalues of ... See full document
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Seidel Signless Laplacian Energy of Graphs
... signless Laplacian eigenvalues have properties fully analogous to those of the ordinary Seidel Laplacians, ...the eigenvalues of the Seidel signless Laplacian matrix satisfy the ... See full document
11
On the Laplacian spectral radii of Halin graphs
... the Laplacian spectral radius of ...Halin graphs with μ (G) ≥ n – 4. Moreover, we obtain the graphs with the first three largest Laplacian spectral radius among all the Halin graphs on n ... See full document
18
Bounds of Eigenvalues of Minor Free Graphs
... In this paper, all graphs are finite undirected graphs without loops and multiple edges. Let G be a graph with n nG vertices, m mG edges, and minimum degree δ or δG. The spectral radius ρG of G is the ... See full document
5
Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls
... In solving the previous three problems, two crucial steps have been employed. The first step is to prove that the extremal values can be attained by some weights. For regular self-adjoint linear Sturm-Liouville problems ... See full document
21
On the set of eigenvalues of a class of equimodular matrices
... of a normal gap in the eigenvalue set of s non-negative matrix A must actually be an eigenvalue of a matrix in ~A • We shall now prove two lemmas which will enable us to use this fact to[r] ... See full document
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Bounding the HL index of a graph: a majorization approach
... The Hückel molecular orbital method (HMO) (see []) is a methodology for the determi- nation of energies of molecular orbitals of π-electrons. It has been shown that π-electron energy levels are strictly related to graph ... See full document
14
The integral equation methods for the perturbed Helmholtz eigenvalue problems
... ple eigenvalues of the unperturbed configuration. These eigenvalues may evolve, under shape deformation, as separated, distinct eigenvalues, and this splitting may only become apparent at high orders ... See full document
20
On a nonresonance condition between the first and the second eigenvalues for the p Laplacian
... [2] , Simplicité et isolation de la première valeur propre du p-Laplacien avec poids [Sim- plicity and isolation of the first eigenvalue of the p-Laplacian with weight], C. R. Acad. Sci. Paris Sér. I Math. 305 ... See full document
10
On the Laplacian Coefficients of Bicyclic Graphs
... the Laplacian coefficients changed after some graph ...about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic ...of graphs based on their Laplacian like ... See full document
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