Results 11 to 20 of about 120 (101)
On distance signless Laplacian spectrum and energy of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2018 The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as DQ(G) = Tr(G) + D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal ...
Abdollah Alhevaz +2 more
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On the eigenvalues of the distance signless Laplacian matrix of graphs
Proyecciones (Antofagasta)Let G be a connected graph and let DQ(G) be the distance signless Laplacian matrix of G with eigenvalues ρ1≥ ρ2≥…≥ ρn. The spread of the matrix DQ}(G) is defined as s(DQ(G)) := maxi,j| ρi-ρj| = ρ1- ρn. We derive new bounds for the distance signless Laplacian spectral radius ρ1 of G.
Akbar Jahanbani +3 more
openaire +2 more sources
Upper and Lower Bounds for the Spectral Radius of Generalized Reciprocal Distance Matrix of a Graph
Mathematics, 2022 For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of G is defined to be RQ(G)=RT(G)+RD(G), where RD(G) is the reciprocal distance matrix, RT(G)=diag(RT1,RT2,⋯,RTn) and RTi is the reciprocal distance ...
Yuzheng Ma, Yubin Gao, Yanling Shao
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Sharp Bounds on (Generalized) Distance Energy of Graphs [PDF]
Mathematics, 2020 Given a simple connected graph G, let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian matrix, D Q ( G ) be the distance signless Laplacian matrix, and T r ( G ) be the vertex transmission ...
Abdollah Alhevaz +3 more
doaj +2 more sources
Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
MathematicsLet X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new
Luis Medina +2 more
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New Bounds for the Generalized Distance Spectral Radius/Energy of Graphs
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Let G be a simple connected graph with vertex set V(G) = {v1, v2, …, vn} and dvi be the degree of the vertex vi. Let D(G) be the distance matrix and Tr(G) be the diagonal matrix of the vertex transmissions of G. The generalized distance matrix of G is defined as Dα(G) = αTr(G) + (1 − α)D(G), where 0 ≤ α ≤ 1. If λ1, λ2, …, λn are the eigenvalues of Dα(G)
Yuzheng Ma +3 more
wiley +1 more source
On Laplacian Equienergetic Signed Graphs
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The Laplacian energy of a signed graph is defined as the sum of the distance of its Laplacian eigenvalues from its average degree. Two signed graphs of the same order are said to be Laplacian equienergetic if their Laplacian energies are equal. In this paper, we present several infinite families of Laplacian equienergetic signed graphs.
Qingyun Tao, Lixin Tao, Yongqiang Fu
wiley +1 more source
Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index
Complexity, Volume 2021, Issue 1, 2021., 2021 A connected graph is called Hamilton‐connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton‐connected is an NP‐complete problem. Hamiltonian and Hamilton‐connected graphs have diverse applications in computer science and electrical engineering.
Sakander Hayat +4 more
wiley +1 more source
Some Chemistry Indices of Clique‐Inserted Graph of a Strongly Regular Graph
Complexity, Volume 2021, Issue 1, 2021., 2021 In this paper, we give the relation between the spectrum of strongly regular graph and its clique‐inserted graph. The Laplacian spectrum and the signless Laplacian spectrum of clique‐inserted graph of strongly regular graph are calculated. We also give formulae expressing the energy, Kirchoff index, and the number of spanning trees of clique‐inserted ...
Chun-Li Kan +4 more
wiley +1 more source
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