Split Legendary Domination in graphs

Abstract

Harary and Norman introduced the line graph L(G) . We introduced the legendary domination number by combining the domination concept both in graph and its line graph. In this paper, the split domination property is studied along with the legendary domination concept. Hence the split legendary dominating set is introduced and the corresponding split legendary domination number is defined for the line graph L(G). Also, the graph theoretical parameters are studied in terms of elements of G and its relationship with other domination parameters are presented.

Keywords

• split domination number, legendary domination number, split legendary domination number.