IWOCA 2012: Combinatorial Algorithms pp 122-124

# Super Connectivity of the Generalized Mycielskian of Graphs

• S. Francis Raj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

## Introduction

All graphs considered in this paper are simple, finite, nontrivial and undirected.

Let G be a graph with vertex set $$V^0=\{v_0^0,v_1^0,\ldots,v_{n-1}^0\}$$ and edge set E 0. Given an integer m ≥ 1, the m-Mycielskian (also known as the generalized Mycielskian) of G, denoted by μ m (G), is the graph whose vertex set is the disjoint union

$$V^0\cup V^1\cup\ldots\cup V^m\cup\{u\},$$
where $$V^i=\{v_j^i;v_j^0\in V^0\}$$ is the i-th copy of V 0, i = 1,2,…,m, and edge set
$$E^0\cup\Big(\mathop{\cup}\limits_{i=0}^{m-1}\{v_j^iv_{j'} ^{i+1}\ :v_j^0v_{j'}^0\in E^0\}\Big)\cup \{v_j^mu: v_j^m\in V^m\}.$$

## Keywords

Mycielskian Generalized Mycielskian Vertex-connectivity Edge- connectivity Super connectivity Super edge connectivity

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## Authors and Affiliations

• S. Francis Raj
• 1
1. 1.Department of MathematicsPondicherry UniversityPuducherryIndia