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On the Alon-Tarsi Number of Some Line and Total graphs

S. Prajnanaswaroopa

Abstract

This work discusses the Alon-Tarsi number of line graphs and total graphs. In addition, we also discuss the Alon-Tarsi number of some Erdos-Faber-Lovasz (EFL) graphs.

On the Alon-Tarsi Number of Some Line and Total graphs

Abstract

This work discusses the Alon-Tarsi number of line graphs and total graphs. In addition, we also discuss the Alon-Tarsi number of some Erdos-Faber-Lovasz (EFL) graphs.
Paper Structure (3 sections, 4 theorems)

This paper contains 3 sections, 4 theorems.

Table of Contents

  1. Abstract
  2. Introduction
  3. Theorems

Key Result

Theorem 1

If $G$ is an $n$ order $1-$ factorizable regular graph with maximum degree $\Delta$ and $n=4k$ for some integer $k$, then $ATN$ of the line graph of $G$ is equal to $n-1$. Hence, the LCC holds for these graphs.

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • proof
  • Theorem 3
  • proof