Results 31 to 40 of about 828 (207)
Burning Numbers of t-unicyclic Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 Given a graph $G$, the burning number of $G$ is the smallest integer $k$ for which there are vertices $x_1, x_2,\ldots,x_k$ such that $(x_1,x_2,\ldots,x_k)$ is a burning sequence of $G$. It has been shown that the graph burning problem is NP-complete, even for trees with maximum degree three, or linear forests. A $t$-unicyclic graph is a unicycle graph
Ruiting Zhang, Yingying Yu, Huiqing Liu
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Null decomposition of unicyclic graphs [PDF]
Discrete Applied Mathematics, 2020 arXiv admin note: text overlap with arXiv:1907 ...
Luiz Emilio Allem +4 more
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Incidence and Laplacian matrices of wheel graphs and their inverses
The American Journal of Combinatorics, 2023 It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs.
Jerad Ipsen, Sudipta Mallik
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Unicyclic components in random graphs [PDF]
Journal of Physics A: Mathematical and General, 2004 4 pages, 2 ...
E. Ben-Naim, Paul L. Krapivsky
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The Signless Laplacian Estrada Index of Unicyclic Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, where q1, q2,..., qn are the eigenvalues of the signless Laplacian matrix of G.
Hamid Reza Ellahi +3 more
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On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth
Journal of Mathematics, 2022 Let G be a graph having the set of edges EG. Represent by dGu the degree of a vertex u of G. The Sombor (SO) index of G is defined as SOG=∑uv∈EGdGu2+dGv2. The length of a shortest cycle in a graph G is known as the girth of G.
B. Senthilkumar +5 more
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Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
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Gallai-Edmonds decomposition of unicyclic graphs from null space [PDF]
The American Journal of Combinatorics, 2022 In this paper, we compute the Gallai-Edmonds decomposition of a unicyclic graph $G$ using linear algebraic tools. More precisely, the Gallai-Edmonds decomposition of $G$ is obtained from the null space associated with adjacency matrices of its subtrees.
Luiz Emilio Allem +3 more
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The inverse of the incidence matrix of a unicyclic graph [PDF]
Linear and Multilinear Algebra, 2022 The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of the inverse of the incidence matrix of an odd unicyclic graph was known.
Hessert, Ryan, Mallik, Sudipta
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Generating graceful unicyclic graphs from a given forest
AKCE International Journal of Graphs and Combinatorics, 2020 Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (
G. Sethuraman, V. Murugan
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