on the total domatic number of regular graphs
نویسندگان
چکیده
a set $s$ of vertices of a graph $g=(v,e)$ without isolated vertex is a {em total dominating set} if every vertex of $v(g)$ is adjacent to some vertex in $s$. the {em total domatic number} of a graph $g$ is the maximum number of total dominating sets into which the vertex set of $g$ can be partitioned. we show that the total domatic number of a random $r$-regular graph is almost surely at most $r-1$, and that for 3-regular random graphs, the total domatic number is almost surely equal to 2. we also give a lower bound on the total domatic number of a graph in terms of order, minimum degree and maximum degree. as a corollary, we obtain the result that the total domatic number of an $r$-regular graph is at least $r/(3ln(r))$.
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عنوان ژورنال:
transactions on combinatoricsناشر: university of isfahan
ISSN 2251-8657
دوره 1
شماره 1 2012
میزبانی شده توسط پلتفرم ابری doprax.com
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