Teresa Haynes

East Tennessee State University; Department of Mathematics

[ 1 ] - Paired-Domination Game Played in Graphs

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...

[ 2 ] - k-Efficient partitions of graphs

A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...

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