On the total domatic number of regular graphs

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August undefined, 2024

WebThe 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 domatic number is almost surely equal to 3. WebRegular 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 …

On The Local Multiset Dimension of some Families of Graphs

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 … in 125 ancine

Upper bounds on the signed total domatic number of graphs

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 … Web28 de abr. de 2011 · The maximum number of functions in a signed total dominating family on G is the signed total domatic number of G, denoted by d t S (G). In this article we … WebIn this section we prove that for all cubic regular graphs, having no subgraph isomorphic to L (given in Figure 1), the total domatic number is at least two. Figure 1: The graph L Theorem 2. The vertex set of a cubic graph can be partitioned into two total dominating sets if it has no subgraph (not necessarily induced) isomorphic to the graph L. in 1252 rfb

(PDF) On Domatic and Total Domatic Numbers of Product Graphs

Signed k,k -domatic number of a graph - CORE

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 ... Webnumber of a graph, where we partition the vertex set into classes having certain properties (in this case, each class is a dominating set). We consider here the fractional analogue … lithonia lxpw-1gWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 in128 inss interativa

"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 … " - On the total domatic number of regular graphs

On the total domatic number of regular graphs

The k-Tuple Domatic Number of a Graph - Semantic Scholar

WebAn (h,k)-dominating set in a digraph G is a subset D of V(G) such that the subdigraph induced by D is h-connected and for every vertex v of G, v is in-dominated and out-dominated by at least k vertices in D. The (h,k)-domination number @c"h","k(G) of G ... 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

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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 equal 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 …

WebThe 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 ... 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 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 …

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 total domatic number of a graph is denoted by and is defined as , where and are the total dominating sets and are the maximum disjoint partition of the vertex set of the graph. ... “On the total domatic number of regular graphs,” Transactions on Combinatorics, vol. 1, no. 1, pp. 45–51, 2012. View at: Google Scholar.

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 …

WebIn this paper we shall study the domatic number, the total domatic number and the connected domatic number of cubic graphs, i. e. regular graphs of degree 3. We … lithonia lxw3relnWeb× Close. The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. in 128/2022 pdfWeb11 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 … lithonia lzn1WebWe 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 … lithonia lxpw-1g-120-elnWeb20 de fev. de 2024 · The fractional domatic number G is defined as F T D ( G) = sup M M r M. In 2024, Goddard and Henning showed that the incidence graph of every complete k -uniform hypergraph H with order n has F T D ( I ( H)) = n n − k + 1 when n ≥ 2 k ≥ 4. We extend the result to the range n > k ≥ 2. in 1300 rfbWebdegree of a vertex in G. (For any graph G the domatic number d(G) < md(G) + 1.) A uniquely domatic graph is a graph G in which there exists exactly one domatic partition with d(G) classes. Analogous concepts may be defined for the total domatic number. A graph G is called totally domatically full, if lithonia m59Web1 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 … in.13.121.t.20