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A Subset S of vertices of a Graph G is called a vertex cover if S includes at least one end point of every edge of the Graph. A Vertex cover S of G is a connected vertex cover if the induced subgraph of S is connected. The minimum cardinality of such a set is called the connected vertex covering number and it is denoted by . A Vertex cover S of G is a total vertex cover if the induced subgraph of S has no isolates. The minimum cardinality of such a set is called the total vertex covering numberdoi:10.17762/turcomat.v12i2.1901 fatcat:xpuxqthnjjh4lj6jrgzkhlhyjm