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On Automorphism Group of a Family of Symmetric Graphs

Sucharita Biswas

Abstract

In this paper, we study the automorphism group and geodesic transitivity of a family of vertex-transitive graphs $H(n,k)$, introduced by Fu-Tao Hu \textit{et.al.} in 2010. In the process, we address some naturally arising, unanswered questions from that paper.

On Automorphism Group of a Family of Symmetric Graphs

Abstract

In this paper, we study the automorphism group and geodesic transitivity of a family of vertex-transitive graphs , introduced by Fu-Tao Hu \textit{et.al.} in 2010. In the process, we address some naturally arising, unanswered questions from that paper.
Paper Structure (9 sections, 8 equations, 2 figures)

This paper contains 9 sections, 8 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions and Preliminaries
  3. When $n=2k-1$
  4. When $k$ is an odd integer and $n=2k+1$
  5. When $k$ is an even integer and $n=2k+1$
  6. When $n \neq 2k-1,2k,2k+1$
  7. Geodesic Transitivity
  8. Open Issues
  9. Acknowledgement

Figures (2)

  • Figure :
  • Figure :

Theorems & Definitions (10)

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