On the total domatic number of regular graphs
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 ... Webalmost surely at most r, and that for 3-regular random graphs, the domatic number is almost surely equal to 3. We also give a lower bound on the domatic number of a …
On the total domatic number of regular graphs
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WebThe 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. Keywords. total dominating set WebThe 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 …
Web1 de jun. de 2024 · DOI: 10.22049/CCO.2024.26125.1078 Corpus ID: 55233617; Double Roman domination and domatic numbers of graphs @inproceedings{Volkmann2024DoubleRD, title={Double Roman domination and domatic numbers of graphs}, author={Lutz Volkmann}, year={2024} }
Web15 de set. de 2024 · For regular graphs with higher minimum degree, we have the following lower bound on the fractional total domatic number of a regular graph. Theorem 31 ([ 16 ]) For all k ≥ 3 , if G is a k-regular graph, then Web14 de set. de 2010 · In this paper we initiate the study of the total {k}-domatic number in graphs and we present some bounds for \(d_{t}^{\{k\}}(G)\). Many of the known bounds …
Web19 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 …
Web1 de abr. de 2011 · In this paper, we prove that the problems of computing the signed domatic number and the signed total domatic number of a given graph are both NP … araraquara x ibitingaWebgraphs. Additionally, we establish similar results for total domatic partitions. Keywords: domatic partitions; graph algorithms; in nite regular graphs; com-putability theory 1 Introduction A set D of vertices in a graph G is called dominating if every vertex of G not in D is adjacent to a vertex in D. bake america egg againWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 bake america egg again apronWebThe domatic number of a graph is the maximum number of dominating sets in a domatic partition of the graph, or equivalently ... Determining if a d-regular graph is domatically full is NP-complete, for any d≥ 3 [34, 23]. Farber [10] showed nonconstructively that strongly chordal graphs are domatically full. This class contains the classes of ... bake and take laudiumWeb11 de jul. de 2024 · The total k-domatic partition problem is to partition the vertices of a graph into k pairwise disjoint total dominating sets. In this paper, we prove that the 4-domatic partition problem is NP-complete for planar graphs of bounded maximum degree. We use this NP-completeness result to show that the total 4-domatic partition problem … araraquara x ibitinga onibusWebThe 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 … bake and makeWebThe 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 … bake and shake bhopal