On the total domatic number of regular graphs
WebIn graph theory, a domatic partition of a graph = (,) is a partition of into disjoint sets , ,..., such that each V i is a dominating set for G.The figure on the right shows a domatic partition of a graph; here the dominating set consists of the yellow vertices, consists of the green vertices, and consists of the blue vertices.. The domatic number is the maximum … WebThe domination number, denoted by γ(G), is the minimum cardinality of a dominating set. In this paper we prove that if G is a 4-regular graph with order n, then γ(G) ≤ 4/11 n Let G …
On the total domatic number of regular graphs
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Web1 de out. de 2004 · We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the domatic number is … WebWe 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 …
WebThe properties of the signed total domatic number d t s (G) are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs. Let G = (V, E) be a graph, and let f: V → {−1, 1} be a two-valued function.
WebWe 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 … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the …
Webclass of regular graphs whose vertices are impossible to be decomposed into two total dominating sets. It is briefly ... which is an open problem. Cubic Graphs with Total Domatic Number at Least Two 77 Since coloring and partitioning are essentially the same, the total domination has also been studied in the literature of graph coloring under ...
Web1 de mar. de 2012 · 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 … cof chemdrawWebRegular total domatically full graphs are also called rainbow graphs (see, [27, 29]). We first make some easy observations on rainbow graphs. Examples of rainbow graphs … calvin township 49031WebThe fractional domatic number of a graph G is the maximum ratio F /m(F) over all families F of dominating sets of G, where m(F) denotes the maximum number of times an element appears in F . The fractional idiomatic and fractional total domatic numbers are defined analogously with F all families of independent dominating sets and total dominating sets … calvin tran robert halfWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 calvin toy reviewWeb19 de mar. de 2024 · In this paper, we show that for two non-trivial graphs $G$ and $H$, the domatic and total domatic numbers of their Cartesian product $G \cart H$ is … cof chargesWeb28 de jun. de 2011 · Semantic Scholar's Logo cofc help deskWebh. aram, s.m. sheikholeslami, and l. volkmann, “on the total domatic number of regular graphs,” transactions on combinatorics, vol. 1, no. 1, pp. 45–51, 2012, [online]. … calvin tran fashion