Results 61 to 70 of about 6,081 (145)
The Generalized Distance Spectrum of the Join of Graphs [PDF]
, 2020 Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) .
Alhevaz, Abdollah +3 more
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AKCE International Journal of Graphs and Combinatorics, 2020 A graph is said to be borderenergetic (-borderenergetic, respectively) if its energy (Laplacian energy, respectively) equals the energy (Laplacian energy, respectively) of the complete graph .
Qingyun Tao, Yaoping Hou
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On the construction of L-equienergetic graphs
AKCE International Journal of Graphs and Combinatorics, 2015 For a graph G with n vertices and m edges, and having Laplacian spectrum μ1,μ2,…,μn and signless Laplacian spectrum μ1+,μ2+,…,μn+, the Laplacian energy and signless Laplacian energy of G are respectively, defined as LE(G)=∑i=1n|μi−2mn| and LE+(G)=∑i=1n ...
S. Pirzada, Hilal A. Ganie
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A Note on Some Bounds of the α‐Estrada Index of Graphs
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0 ≤ α ≤ 1 and A(G) and D(G) denote the adjacency matrix and degree matrix of G, respectively. EEαG=∑i=1neλi is called the α‐Estrada index of G, where λ1, ⋯, λn denote the eigenvalues of A~αG. In this paper, the upper and lower bounds for EEα(G) are given.
Yang Yang +3 more
wiley +1 more source
Bounds for the Generalized Distance Eigenvalues of a Graph [PDF]
, 2019 Let G be a simple undirected graph containing n vertices. Assume G is connected. Let D(G) be the distance matrix, DL(G) be the distance Laplacian, DQ(G) be the distance signless Laplacian, and Tr(G) be the diagonal matrix of the vertex transmissions ...
Alhevaz, Abdollah +3 more
core +1 more source
Construction for the Sequences of Q‐Borderenergetic Graphs
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This research intends to construct a signless Laplacian spectrum of the complement of any k‐regular graph G with order n. Through application of the join of two arbitrary graphs, a new class of Q‐borderenergetic graphs is determined with proof. As indicated in the research, with a regular Q‐borderenergetic graph, sequences of regular Q‐borderenergetic ...
Bo Deng +4 more
wiley +1 more source
Parabolic theory of the discrete p-Laplace operator [PDF]
, 2013 We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem.
Mugnolo, Delio
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Bounds on the α‐Distance Energy and α‐Distance Estrada Index of Graphs
Discrete Dynamics in Nature and Society, Volume 2020, Issue 1, 2020., 2020 Let G be a simple undirected connected graph, then Dα(G) = αTr(G) + (1 − α)D(G) is called the α‐distance matrix of G, where α ∈ [0,1], D(G) is the distance matrix of G, and Tr(G) is the vertex transmission diagonal matrix of G. In this paper, we study some bounds on the α‐distance energy and α‐distance Estrada index of G.
Yang Yang +3 more
wiley +1 more source
Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph
Mathematics, 2023 Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix,
Shaun Fallat, Seyed Ahmad Mojallal
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Energy, Laplacian energy of double graphs and new families of equienergetic graphs [PDF]
, 2014 For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G* is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or
Ganie, Hilal A. +2 more
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