THE FORCING DETOUR DOMINATION DEGREE NUMBER OF A GRAPH

Abstract

Let G be a connected graph and S is a minimum detour dominating degree set of G.A subset T⊆S is called a forcing subset of S if S is the unique minimum detour dominating degree set containing T.A forcing subset for S of minimum cardinality is a minimum forcing subset of S .The forcing detour dominating degree number of S, denoted by fγdd(G),is the cardinality of a minimum forcing subset of S but the forcing detour domination degree number denoted fγdd(G) =mini{ fγdd(G)} = max{ld(S)}=max{deg(u)+deg(v)+∑deg(w) }where the minimum is taken over all minimum detour dominating degree set S in G but in the mini fγdd(S) we find the max{ld(G)} in G.