ON CONNECTED GLOBAL OFFENSIVE k-ALLIANCE NUMBER OF SOME GRAPHS
Inspired by the study of Lutz Volkmann of RWTH Aachen University in Germany, this paper focuses on the connected global offensive k-alliances in graphs. Considering finite graphs G with vertex-set we define by the subgraph induced by S for a subset Let k be a positive integer. A subset is a connected global offensive k-alliance of the connected graph G, if the induced subgraph of S is connected and for every vertex where is the neighborhood of v. The connected global offensive k-alliance number is the minimum cardinality of a connected global offensive k-alliance in G. A connected global offensive k-alliance set of the minimum cardinality of a connected graph G is called a -set. Further, some of the connected global offensive k-alliance numbers of fan graphs, wheel graphs, join of path graphs, and friendship graphs are characterized.
connected global offensive k-alliance numbers, k-alliance number.