Applied Mathematical Sciences, Vol. 9, 2015, no. 115, 5707 - 5714 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.56455 Revisiting the Vertex Cover of Graphs Joselito A. Uy Department of Mathematics and Statistics MSU-Iligan Institute of Technology Iligan City, Philippines Vinessa P. Abregana Nueva Vista National High School Don Victoriano, Misamis Occidental, Philippines Copyright c  2015 Joselito A. Uy and Vinessa P. Abregana. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribu- tion, and reproduction in any medium, provided the original work is properly cited. Abstract A set U of vertices of graph G is a vertex cover of G if every edge in G is incident with a vertex in U . The minimum cardinality of such set is the vertex covering number of G and is denoted by α(G). This paper characterizes bipartite graphs in terms of vertex cover. It provides the vertex covering number of (i) the complement of a nonempty bipartite graph, (ii) the powers of paths and cycles, and (iii) one supergraph of planar grid. Keywords: vertex cover, bipartite graph, power of graph, planar grid 1 Introduction In this paper, vertex set and edge set of a graph G are denoted by V G and E G , respectively. If an edge joins vertices x and y, it is denoted by xy. For other definitions and notations used in this paper, the reader is referred to [5]. Definition 1.1 A set U of vertices of graph G is a vertex cover of G if every edge in G is incident with a vertex in U . The minimum cardinality of such set is the vertex covering number of G and is denoted by α(G).