ISSN 0976-5727 (Print) ISSN 2319-8133 (Online) Abbr:J.Comp.&Math.Sci. 2014, Vol.5(2): Pg.141-149 JOURNAL OF COMPUTER AND MATHEMATICAL SCIENCES An International Open Free Access, Peer Reviewed Research Journal www.compmath-journal.org Journal of Computer and Mathematical Sciences Vol. 5, Issue 2, 30 April, 2014 Pages (123 - 257) A Study on Minimum Covering of Invertible Trees Amutha A. 1 and Angel D. 2 1 Assistant Professor, Department of Mathematics, Sathyabama University, Chennai, INDIA. 2 Research Scholar, Department of Mathematics, Sathyabama University, Chennai, INDIA. (Received on: February 14, 2014) 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. 1. INTRODUCTION The covering and the inverse covering parameters play a vital role in coding theory, computer science, operations research, switching circuits, electrical networks etc. 4 . One of the best studied graph problems in theoretical computer science is the vertex cover problem which is a special class of the set cover problem. The vertex cover problem has many real world applications. An interesting field of application of the vertex cover problem is in bio-informatics, in the construction of polygenetic trees, in phenotype identification and in analysis of micro array data. It is also