On Matching Girth Domination Number of Graphs

A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. A set S of vertices in G is a girth dominating set of G if every vertex in V-S is adjacent to atleast one vertex of girth graph is called the girth dominating set. the matching number is the maximum cardinality of a matching of G, while the girth domination number of G is the minimum cardinality taken over all girth domination number and is denoted by _g (G) also the addition of any edge decreases the girth domination number denoted by _mg (G).