Results 41 to 50 of about 5,819 (125)
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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Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Trends in Computational and Applied Mathematics, 2021 We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga +2 more
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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
Theory and Applications of Graphs, 2021 In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent.
Dhiren Basnet, Ajay Sharma, Rahul Dutta
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Signless Laplacian determinations of some graphs with independent edges
Karpatsʹkì Matematičnì Publìkacìï, 2018 Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of $G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix and the adjacency matrix of $G$, respectively.
R. Sharafdini, A.Z. Abdian
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Cospectral constructions for several graph matrices using cousin vertices
Special Matrices, 2021 Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum.
Lorenzen Kate
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A novel method to construct cospectral graphs based on RT operation [PDF]
AIP AdvancesThis paper presents a new graph operation, RT(G), which is formed by transforming each vertex and edge of the original graph G into a triangle. We analyze the relationship between the signless Laplacian characteristic polynomials of the graph RT(G) and ...
Xiu-Jian Wang +2 more
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Color signless Laplacian energy of graphs
AKCE International Journal of Graphs and Combinatorics, 2017 In this paper, we introduce the new concept of color Signless Laplacian energy . It depends on the underlying graph and the colors of the vertices. Moreover, we compute color signless Laplacian spectrum and the color signless Laplacian energy of families
Pradeep G. Bhat, Sabitha D’Souza
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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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On the sum of signless Laplacian spectra of graphs
Karpatsʹkì Matematičnì Publìkacìï, 2019 For a simple graph $G(V,E)$ with $n$ vertices, $m$ edges, vertex set $V(G)=\{v_1, v_2, \dots, v_n\}$ and edge set $E(G)=\{e_1, e_2,\dots, e_m\}$, the adjacency matrix $A=(a_{ij})$ of $G$ is a $(0, 1)$-square matrix of order $n$ whose $(i,j)$-entry is ...
S. Pirzada, H.A. Ganie, A.M. Alghamdi
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