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Domination Numbers and Automorphisms of Dual Graphs Over Vector Spaces

  • Long Wang
Article
  • 27 Downloads

Abstract

Let \(F_q\) be a finite field of q elements, \(\mathbb {V}\) an n-dimensional vector space over \(F_q\), and \(\mathbb {V}^*\) the dual space of \(\mathbb {V}\), i.e., the vector space of all linear function over \(\mathbb {V}\). The graph \(\hbox {DG}(\mathbb {V})\), called the dual graph of \(\mathbb {V}\), is defined to be a bipartite graph, whose vertex set is partitioned into two coloring sets, respectively, consisting of all one-dimensional subspaces of \(\mathbb {V}\) and all one-dimensional subspaces of \(\mathbb {V}^*\), and there is an undirected edge between an one-dimensional subspace [v] of \(\mathbb {V}\) and an one-dimensional subspace [f] of \(\mathbb {V}^*\) if and only if \(f(v) = 0\). In this paper, the domination number, independence number, diameter and girth of \(\hbox {DG}(\mathbb {V})\) are, respectively, determined; some automorphisms of \(\hbox {DG}(\mathbb {V})\) are introduced, and such a graph is proved to be distance transitive.

Keywords

Domination number of graphs Automorphisms of graphs Distance-transitive graphs 

Mathematics Subject Classification

05C25 05C69 20H20 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.School of Mathematics and Big DataAnhui University of Science and TechnologyHuinanChina

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