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arXiv · 1903.01324

Uniform Length Dominating Sequence Graphs

Aysel Erey
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Abstract

A sequence of vertices $(v_1,\, \dots , \,v_k)$ of a graph $G$ is called a {\it dominating closed neighborhood sequence} if $\{v_1,\, \dots , \,v_k\}$ is a dominating set of $G$ and $N[v_i]\nsubseteq \cup _{j=1}^{i-1} N[v_j]$ for every $i$. A graph $G$ is said to be {\it $k-$uniform} if all dominating closed neighborhood sequences have equal length $k$. Bre{\v s}ar et al. (2014) characterized $k$-uniform graphs with $k\leq 3$. In this article we extend their work by giving a complete characterization of all $k$-uniform graphs with $k\geq 4$.

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Aysel Erey. 2020-11-06. Uniform Length Dominating Sequence Graphs. https://doi.org/10.1007/s00373-020-02221-5

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