Majority vertex (edge) cover of a graph

A vertex and an edge are said to cover each other if they are incident. A vertex cover of G is a set of vertices that cover all the edges of G. The smallest number of edges in any vertex cover of G is called the vertex covering number of G and is denoted by alpha(0)(G). A set of edges which cover all the vertices of G is called a edge cover of G. The smallest number of edges in any edge cover of G is called the edge covering number of G and is denoted by alpha(1)(G).