Abstract

A Study on Minimum Covering of Invertible Trees

Amutha A.1 and Angel D.2

1Assistant Professor,
Department of Mathematics,
Sathyabama University, Chennai, INDIA.
2Research Scholar,
Department of Mathematics,
Sathyabama University, Chennai, INDIA.

ABSTRACT

A set S of vertices of a graph G = (V,E) is called a vertex cover if each edge in E has at least one endpoint in S and the minimum cardinality takenover all vertex covering sets of G is called vertex covering number denoted by β(G). In this paper we have obtained a necessary condition for trees to be invertible and also calculated the exact values of the covering and inverse covering numbersof invertible and factor critical trees and hence the relation between the covering parameters of trees such as paths, stars, centipedes and banana trees are obtained.

2010 Mathematics Subject Classification: Primary: 05C76;
Secondary: 05C69.

Keywords :vertex cover, edge cover, inverse cover, invertible trees.

map1 map2 map3