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The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where each $V_i$ is an $i$-packing. In this paper, we investigate for a given tri
Externí odkaz:
http://arxiv.org/abs/1707.04910
In 1970, Plummer defined a well-covered graph to be a graph $G$ in which all maximal independent sets are in fact maximum. Later Hartnell and Rall showed that if the Cartesian product $G \Box H$ is well-covered, then at least one of $G$ or $H$ is wel
Externí odkaz:
http://arxiv.org/abs/1703.08716
The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that there exists a $k$-vertex coloring of $G$ in which any two vertices receiving color $i$ are at distance at least $i+1$. It is proved that in the class
Externí odkaz:
http://arxiv.org/abs/1608.05577
The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $\Pi_1,\ldots,\Pi_k$, where $\Pi_i$, $i\in [k]$, is an $i$-packing. The following conjecture is pose
Externí odkaz:
http://arxiv.org/abs/1608.05573
Autor:
Skardal, Per Sebastian, Wash, Kirsti
Publikováno v:
Phys. Rev. E 94, 052311 (2016)
The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product. Here we study the eigenvalue spectrum of the ad
Externí odkaz:
http://arxiv.org/abs/1606.03930
Autor:
Rall, Douglas F., Wash, Kirsti
An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in a graph $G
Externí odkaz:
http://arxiv.org/abs/1602.04089
Autor:
Henning, Michael A., Wash, Kirsti
Let $G$ be a graph with no isolated vertex. A matching in $G$ is a set of edges that are pairwise not adjacent in $G$, while the matching number, $\alpha'(G)$, of $G$ is the maximum size of a matching in $G$. The path covering number, $\rm{pc}(G)$, o
Externí odkaz:
http://arxiv.org/abs/1501.04679
Autor:
Henning, Michael A., Wash, Kirsti
In this paper, we continue the study of neighborhood total domination in graphs first studied by Arumugam and Sivagnanam [Opuscula Math. 31 (2011), 519--531]. A neighborhood total dominating set, abbreviated NTD-set, in a graph $G$ is a dominating se
Externí odkaz:
http://arxiv.org/abs/1408.0109
Autor:
Wash, Kirsti
Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi$ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi(u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the
Externí odkaz:
http://arxiv.org/abs/1308.5466