GEODETIC DOMINATION NUMBER OF MYCIELSKI GRAPH - Sukma Alam, Muhammad
For any graph G the set of vertices is denoted by V (G) and the edge set by E(G). A vertex in graph G dominates itself and neighbors. A set of vertices D in graph G is a dominating set if each vertex of G is dominated by some vertex of D. A x-y path of length d(x, y) is called x-y geodesic. The closed interval I[x, y] consist of x, y and all vertices lying on some x-y geodesic of G. A set S of vertices is a geodetic set if I[S] = V (G). A subset W of vertices in a graph G is called a geodetic domination set if W is both a geodetic set and a dominating set. The minimum cardinality of a geodetic domination of G is geodetic domination number, denoted by γg(G). In this paper, we study the geodetic domination number on Mycielski graphs. We provide the lower and upper bounds of the geodetic domination number on Mycielski of any connected graphs.