Hausdorff property of G^++−, G^+−+ and their complement graphs

Angel Jebitha M K,Nisa Y

doi:10.26524/cm62

Abstract

A simple graph G is said to be Hausdorff graph if for any two vertices u and v of G satisfy at least one of the following conditions: [1] both u and v are isolated [2] either u or v is isolated[3] there exists two non-adjacent edges e1 and e2 of G such that e1 is incident with u and e2is incident with v. In this paper, we discuss Hausdorff property on some specific transformationgraphs namely G++-, G+-+, G--+ and G-+- .

Highlights

In [10], Wu Baoyindureng and Meng Jixiang introduced and studied eight types of transformation graph
The transformation graph Gxyz is the graph having V (G) ∪ E(G) as the vertex set, and for α, β ∈ V (G) ∪ E(G), α and β are adjacent in Gxyz if and only if one of the following holds: (i) for α, β ∈ V (G), α and β are adjacent in G if x=+; α and β are not adjacent in G if x=-.(ii) for α, β ∈ E(G), α and β are adjacent in G if y=+; α and β are not adjacent in G if y=-.(iii) for α ∈ V (G), β ∈ E(G), α and β are incident in G if z=+; α and β are not incident in G if z=
Since G is a connected graph of order n ≥ 4, there exists a vertex u3 adjacent to u1 or u2 in G

Summary

Introduction

In [10], Wu Baoyindureng and Meng Jixiang introduced and studied eight types of transformation graph. Theorem 2.3 Let G be a graph of order n ≥ 3 containing at least one edge.

Results

Conclusion