On the fixed number of graphs
نویسندگان
چکیده مقاله:
A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fixing number and fixed number are both $k$. In this paper, we study the fixed number of a graph and give a construction of a graph of higher fixed number from a graph of lower fixed number. We find the bound on $k$ in terms of the diameter $d$ of a distance-transitive $k$-fixed graph.
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عنوان ژورنال
دوره 43 شماره 7
صفحات 2281- 2292
تاریخ انتشار 2017-12-30
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