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pro vyhledávání: '"Xu, Leyou"'
What spectral conditions imply a graph contains a chorded cycle? This question was asked by R.J. Gould in 2022. We answer three modified versions of Gould's question by giving tight spectral conditions that imply the existence of doubly chorded cycle
Externí odkaz:
http://arxiv.org/abs/2406.17820
A chorded cycle is a cycle with at least one chord. Gould asked in [Graphs Comb. 38 (2022) 189] the question: What spectral conditions imply a graph contains a chorded cycle? For a graph with fixed size, extremal spectral conditions are given to ensu
Externí odkaz:
http://arxiv.org/abs/2405.03229
Let $G$ be a simple graph of order $n$. It is known that any Laplacian eigenvalue of $G$ belongs to the interval $[0,n]$. For an interval $I\subseteq [0, n]$, denote by $m_GI$ the number of Laplacian eigenvalues of $G$ in $I$, counted with multiplici
Externí odkaz:
http://arxiv.org/abs/2401.03777
Answers are offered to the Gould's question to find spectral sufficient conditions for a graph to have a chorded cycle via signless Laplacian spectral radius. The conditions are tight.
Externí odkaz:
http://arxiv.org/abs/2312.16795
For a simple graph on $n$ vertices, any of its signless Laplacian eigenvalues is in the interval $[0, 2n-2]$. In this paper, we give relationships between the number of signless Laplacian eigenvalues in specific intervals in $[0, 2n-2]$ and graph inv
Externí odkaz:
http://arxiv.org/abs/2312.04797
Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It measures the vulnerability even when the removal of links does not discon
Externí odkaz:
http://arxiv.org/abs/2311.02571
A graph is $t$-tough if the deletion of any set of, say, $m$ vertices from the graph leaves a graph with at most $\frac{m}{t}$ components. In 1973, Chv\'{a}tal suggested the problem of relating toughness to factors in graphs. In 1985, Enomoto et al.
Externí odkaz:
http://arxiv.org/abs/2310.10183
The well known Wagner's theorem states that a graph is a planar graph if and only if it is $K_5$-minor-free and $K_{3,3}$-minor-free. Denote by $AT(G)$ the Alon-Tarsi number of a graph $G$. We show that for any $K_{3,3}$-minor-free graph $G$, $AT(G)\
Externí odkaz:
http://arxiv.org/abs/2310.07445
Let $G$ be a connected graph on $n$ vertices with diameter $d$. It is known that if $2\le d\le n-2$, there are at most $n-d$ Laplacian eigenvalues in the interval $[n-d+2, n]$. In this paper, we show that if $1\le d\le n-3$, there are at most $n-d+1$
Externí odkaz:
http://arxiv.org/abs/2306.14127
For $S\subseteq V(G)$ with $|S|\ge 2$, let $\kappa_G (S)$ denote the maximum number of internally disjoint trees connecting $S$ in $G$. For $2\le k\le n$, the generalized $k$-connectivity $\kappa_k(G)$ of an $n$-vertex connected graph $G$ is defined
Externí odkaz:
http://arxiv.org/abs/2303.13864