Pitchfork Domination and It`s Inverse for Corona and Join Operations in Graphs

Authors : Mohammed A ABDLHUSEİN, Manal N ALHARERE

Pages : 51-55

View : 109 | Download : 8

Publication Date : 2019-12-29

Article Type : Research Paper

Abstract :Let $G$ be a finite simple and undirected graph without isolated vertices. A subset $D$ of $V$ is a pitchfork dominating set if every vertex $v \in D$  dominates at least $j$ and at most $k$ vertices of $V-D$, where $j$ and $k$  are non-negative integers .The domination number of $G$, denoted by $\gamma_{pf}insert ignore into journalissuearticles values(G);$ is a minimum cardinality over all pitchfork dominating sets in $G$. A subset $D^{-1}$ of $V-D$ is an  inverse pitchfork dominating set if $D^{-1}$ is a pitchfork dominating set.  The inverse domination number of $G$, denoted by $\gamma_{pf}^{-1}insert ignore into journalissuearticles values(G);$ is a minimum cardinality over all inverse pitchfork  dominating sets in $G$. In this paper, the pitchfork domination and the inverse pitchfork domination are determined when $j=1$ and $k=2$ for some graphs that obtained from graph operations  corona and join.
Keywords : pitchfork domination

ORIGINAL ARTICLE URL