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pro vyhledávání: '"Akbari, S"'
Let $G$ be a graph. A total dominating set in a graph $G$ is a set $S$ of vertices of $G$ such that every vertex in $G$ is adjacent to a vertex in $S$. Recently, the following question was proposed: "Is it true that every connected cubic graph contai
Externí odkaz:
http://arxiv.org/abs/2308.15114
Let $G$ be a connected graph of order $n$ with domination number $\gamma(G)$. Wang, Yan, Fang, Geng and Tian [Linear Algebra Appl. 607 (2020), 307-318] showed that for any Laplacian eigenvalue $\lambda$ of $G$ with multiplicity $m_G(\lambda)$, it hol
Externí odkaz:
http://arxiv.org/abs/2109.06269
Publikováno v:
In Discrete Applied Mathematics 15 July 2024 351:105-110
Publikováno v:
In Geoenergy Science and Engineering July 2024 238
A set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in $S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The independent domination number $i(G)$ of $G$
Externí odkaz:
http://arxiv.org/abs/2001.02946
Let $G$ be a graph of order $n$. The path decomposition of $G$ is a set of disjoint paths, say $\mathcal{P}$, which cover all vertices of $G$. If all paths are induced paths in $G$, then we say $\mathcal{P}$ is an induced path decomposition of $G$. M
Externí odkaz:
http://arxiv.org/abs/1912.00322
Akademický článek
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Publikováno v:
In Linear Algebra and Its Applications 15 November 2023 677:221-236
In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. H
Externí odkaz:
http://arxiv.org/abs/1907.11482
A proper vertex coloring of a graph $G$ is called a star coloring if every two color classes induce a forest whose each component is a star, which means there is no bicolored $P_4$ in $G$. In this paper, we show that the Cartesian product of any two
Externí odkaz:
http://arxiv.org/abs/1906.06561