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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
wiley +1 more source
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 Let G be a graph with n vertices, and let L(G) and Q(G) denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic matrix of L(G) (respectively, Q(G)).
Tingzeng Wu +2 more
wiley +1 more source
Signless Laplacian energies of non-commuting graphs of finite groups and related results [PDF]
Discret. Math. Algorithms Appl., 2023 The non-commuting graph of a non-abelian group $G$ with center $Z(G)$ is a simple undirected graph whose vertex set is $G\setminus Z(G)$ and two vertices $x, y$ are adjacent if $xy \ne yx$.
Monalisha Sharma, R. K. Nath
semanticscholar +1 more source
Nordhaus-Gaddum Type Inequalities for Laplacian and Signless Laplacian Eigenvalues [PDF]
The Electronic Journal of Combinatorics, 2014 Let $G$ be a graph with $n$ vertices. We denote the largest signless Laplacian eigenvalue of $G$ by $q_1(G)$ and Laplacian eigenvalues of $G$ by $\mu_1(G)\ge\cdots\ge\mu_{n-1}(G)\ge\mu_n(G)=0$. It is a conjecture on Laplacian spread of graphs that $\mu_1(G)-\mu_{n-1}(G)\le n-1$ or equivalently $\mu_1(G)+\mu_1(\overline G)\le2n-1$.
Ashraf, F., Tayfeh-Rezaie, B.
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Distance (signless) Laplacian spectrum of dumbbell graphs
Transactions on Combinatorics, 2022 Summary: In this paper, we determine the distance Laplacian and distance signless Laplacian spectrum of generalized wheel graphs and a new class of graphs called dumbbell graphs.
Desikan, Kalyani +1 more
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Linear Algebra and its Applications, 2010 The signless Laplacian spread of \(G\) is defined as \(SQ(G) = \mu_1 (G) - \mu_n (G)\), where \(\mu_1 (G)\) and \(\mu_n (G)\) are the maximum and minimum eigenvalues of the signless Laplacian matrix of \(G\), respectively. This paper presents some upper and lower bounds for \(SQ(G)\). Moreover, the unique unicyclic graph with maximum signless Laplacian
Liu, Muhuo, Liu, Bolian
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Principal eigenvector of the signless Laplacian matrix [PDF]
Computational and Applied Mathematics, 2021 In this paper, we study the entries of the principal eigenvector of the signless Laplacian matrix of a hypergraph. More precisely, we obtain bounds for this entries. These bounds are computed trough other important parameters, such as spectral radius, maximum and minimum degree.
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Signless Laplacian Energy of Interval-Valued Fuzzy Graph and its Applications
Sains Malaysiana, 2023 An interval-valued fuzzy graph (IVFG) emanates from a fuzzy graph (FG) where the membership is given in interval form. This framework give the user more flexibility in dealing with fuzzy information.
M. Romdhini +4 more
semanticscholar +1 more source