Abstract
A Hausdorff graph G is a simple graph in which any two vertices u and v of G satisfy atleast one of the following conditions: (i) both u and v are isolated vertices (ii) either u or v is an isolated vertex (iii) there exists two non-adjacent edges e1 and e2 of G such that e1 is incident with u and e2 is incident with v. In this paper, we investigate Hausdorff property on transformation graphs.
Highlights
In [5], eight types of transformation graph were introduced and their basic properties were studied
Several authors have worked on these eight types of transformation graph separately
Theorem 2.1 The transformation graph G+++ of a graph G is Hausdorff if and only if G has no copy of K2 as a component
Summary
In [5], eight types of transformation graph were introduced and their basic properties were studied. A Hausdorff graph G is a simple graph in which any two vertices u and v of G satisfy atleast one of the following conditions: (i) both u and v are isolated vertices (ii) either u or v is an isolated vertex (iii) there exists two non-adjacent edges e1 and e2 of G such that e1 [3] Any Hamiltonian graph with more than 3 vertices is Hausdorff. Theorem 2.1 The transformation graph G+++ of a graph G is Hausdorff if and only if G has no copy of K2 as a component.
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