Results 31 to 40 of about 960 (155)
Maximizing the signless Laplacian spectral radius of some theta graphs [PDF]
Let $Q(G)=D(G)+A(G)$ be the signless Laplacian matrix of a simple graph $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix of $G$, respectively. The largest eigenvalue of $Q(G)$, denoted by $q(G)$, is called the signless Laplacian spectral radius of $G$.
Yuxiang Liu, Ligong Wang
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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
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Sufficient Conditions for Graphs to Be k‐Connected, Maximally Connected, and Super‐Connected
Complexity, Volume 2021, Issue 1, 2021., 2021 Let G be a connected graph with minimum degree δ(G) and vertex‐connectivity κ(G). The graph G is k‐connected if κ(G) ≥ k, maximally connected if κ(G) = δ(G), and super‐connected if every minimum vertex‐cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k‐connected ...
Zhen-Mu Hong +4 more
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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
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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
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The Randić index and signless Laplacian spectral radius of graphs [PDF]
Discrete Mathematics, 2019 Given a connected graph $G$, the Randi index $R(G)$ is the sum of $\tfrac{1}{\sqrt{d(u)d(v)}}$ over all edges $\{u,v\}$ of $G$, where $d(u)$ and $d(v)$ are the degree of vertices $u$ and $v$ respectively. Let $q(G)$ be the largest eigenvalue of the singless Laplacian matrix of $G$ and $n=|V(G)|$. Hansen and Lucas (2010) made the following conjecture:
Bo Ning, Xing Peng
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Some inequalities involving the distance signless Laplacian eigenvalues of graphs [PDF]
Transactions on Combinatorics, 2021 Given a simple graph $G$, the distance signlesss Laplacian $D^{Q}(G)=Tr(G)+D(G)$ is the sum of vertex transmissions matrix $Tr(G)$ and distance matrix $D(G)$.
Abdollah Alhevaz +3 more
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Some upper bounds for the signless Laplacian spectral radius of digraphs [PDF]
Transactions on Combinatorics, 2019 Let $G=(V(G),E(G))$ be a digraph without loops and multiarcs, where $V(G)=\{v_1,v_2,$ $\ldots,v_n\}$ and $E(G)$ are the vertex set and the arc set of $G$, respectively. Let $d_i^{+}$ be the outdegree of the vertex $v_i$.
Weige Xi, Ligong Wang
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Journal of Inequalities and Applications, 2020 In this paper, we obtain a sharp upper bound on the spectral radius of a nonnegative k-uniform tensor and characterize when this bound is achieved. Furthermore, this result deduces the main result in [X. Duan and B.
Chuang Lv, Lihua You, Xiao-Dong Zhang
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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