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 [SIAM J. Discrete Math. 24 (2010) 979--991]. 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 …
[ 2 ] - k-Efficient partitions of graphs
A set $S = \{u_1,u_2, \ldots, u_t\}$ of vertices of $G$ is an efficient dominating set if every vertex of $G$ is dominated exactly once by the vertices 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 set of $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices at distance~1 from it in $G$. I…
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