Detour Global Domination for Degree Splitting graphs of some graphs

C. Jayasekaran, S.V. Ashwin Prakash


In this paper, we introduced the new concept detour global domination number for degree splitting graph of standard graphs. The detour global dominating sets in some standard and special graphs are determined. First we recollect the concept of degree splitting graph of a graph and we produce some results based on the detour global domination number of degree splitting graph of star graph, bistar graph, complete bipartite graph, complete graph path graph, cycle graph, wheel graph and helm graph. A set S is called a detour global dominating set of G if S is both detour and global dominating set of G. The detour global domination number is the minimum cardinality of a detour global dominating set in G.


Detour set, Dominating set, Detour Domination, Global Domination, Detour Global Domination, Degree Splitting graphs

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