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The $n$-Queens graph, $\mathcal{Q}(n)$, is the graph obtained from a $n\times n$ chessboard where each of its $n^2$ squares is a vertex and two vertices are adjacent if and only if they are in the same row, column or diagonal. In a previous work the
Externí odkaz:
http://arxiv.org/abs/2301.08106
Publikováno v:
In Discrete Mathematics September 2024 347(9)
Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the
Externí odkaz:
http://arxiv.org/abs/2201.01224
A caterpillar graph $T(p_1, \ldots, p_r)$ of order $n= r+\sum_{i=1}^r p_i$, $r\geq 2$, is a tree such that removing all its pendent vertices gives rise to a path of order $r$. In this paper we establish a necessary and sufficient condition for a real
Externí odkaz:
http://arxiv.org/abs/2107.11422
The $H$-join of a family of graphs $\mathcal{G}=\{G_1, \dots, G_p\}$, also called the generalized composition, $H[G_1, \dots, G_p]$, where all graphs are undirected, simple and finite, is the graph obtained by replacing each vertex $i$ of $H$ by $G_i
Externí odkaz:
http://arxiv.org/abs/2101.08383
A vertex $v \in V(G)$ is called $\lambda$-main if it belongs to a star set $X \subset V(G)$ of the eigenvalue $\lambda$ of a graph $G$ and this eigenvalue is main for the graph obtained from $G$ by deleting all the vertices in $X \setminus \{v\}$; ot
Externí odkaz:
http://arxiv.org/abs/2012.10969
The $n$-Queens' graph, $\mathcal{Q}(n)$, is the graph associated to the $n \times n$ chessboard (a generalization of the classical $8 \times 8$ chessboard), with $n^2$ vertices, each one corresponding to a square of the chessboard. Two vertices of $\
Externí odkaz:
http://arxiv.org/abs/2012.01992
Akademický článek
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Autor:
Cardoso, Domingos M.
Publikováno v:
Discrete Applied Mathematics, 2019
A ($\kappa$,$\tau$)-regular set is a vertex subset S inducing a $\kappa$-regular subgraph such that every vertex out of S has $\tau$ neighbors in S. This article is an expository overview of the main results obtained for graphs with ($\kappa$,$\tau$)
Externí odkaz:
http://arxiv.org/abs/1812.11895
Autor:
Cardoso, Domingos M.
A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number was intro
Externí odkaz:
http://arxiv.org/abs/1811.05516