On Sombor Domination in Graphs

Abstract

For a simple graph , a subset  is a dominating set if , where  denote the open neighborhood of the set . The Sombor index  of a graph  is the sum of square root of squares of degrees of every end-vertex of an edge  in . In this paper, these two classical concepts are combined and initia

For a simple graph , a subset  is a dominating set if , where  denote the open neighborhood of the set . The Sombor index  of a graph  is the sum of square root of squares of degrees of every end-vertex of an edge  in . In this paper, these two classical concepts are combined and initiated the study of Sombor-domination number  of a graph . Further, some upper and lower bounds are obtained for  in terms of other graph theocratical parameters. Finally, we conclude this paper by showing applications of  in QSPR-studies of alkanes.

ted the study of Sombor-domination number  of a graph . Further, some upper and lower bounds are obtained for  in terms of other graph theocratical parameters. Finally, we conclude this paper by showing applications of  in QSPR-studies of alkanes.