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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 … Webdegree 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

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

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 Web24 de dez. de 2001 · 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 … mobility plus gutter frame walker https://bayareapaintntile.net

Fractional Domatic, Idomatic, and Total Domatic Numbers of a …

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 … Web14 de set. de 2010 · The total {. k. }-domatic number of a graph. For a positive integer k, a total { k }- dominating function of a graph G is a function f from the vertex set V ( G) to the set {0,1,2,…, k } such that for any vertex v ∈ V ( G ), the condition ∑ u∈N(v) f ( u )≥ k is fulfilled, where N ( v) is the open neighborhood of v. Web20 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. ink master texas

On the total domatic number of regular graphs – DOAJ

Category:CubicGraphswithTotalDomaticNumberatLeastTwo - arXiv

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On the total domatic number of regular graphs

Fractional Domatic, Idomatic and Total Domatic Numbers of a Graph

WebG is the signed (k,k)-domatic number of G, denoted by dk S(G). First we study basic properties of dk S(G). Some of them are extensions of well-known results on the signed domatic number dS(G) = d1 S(G) given in [6]. Using these results, we determine the signed (k,k)-domatic numbers of fans, wheels and grids. 2. Basic properties of the signed (k ... WebAbstract: A circulant graph is a Cayley graph constructed out of a finite cyclic group Γ and a generating set A is a subset of Γ. In this paper, we attempt to find upper bounds for distance-g domination, distance-g paired domination and distance-g connected domination number for circulant graphs. Exact values are also determined in certain cases.

On the total domatic number of regular graphs

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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 ... 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 …

Webh. 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]. … Web1 de abr. de 2006 · In this paper, we define the signed total domatic number of a graph in an analogous way to that of the fractional domatic number defined by D. F. Rall [Congr. …

WebOther known results are, dimensions at least 3 were proven by Bong et al., for example, the 𝑚-shadow graph by Adawiyah et [12], for almost hypercube graphs by Alfarisi et al., al., [8], and the local multiset dimension of [5], trees by Hafidh et al., [11], starphene and unicyclic graphs was also studied by Adawiyah et zigzag-edge coronoid by Liu et al., [13]. 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} }

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mobilityplus+ lightweight electric wheelchairWeb× 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. mobility plus north las vegasWeb11 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 … ink master winner season 12WebWe 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 … ink master tucsonWebIn 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. mobility plus lightweight electric wheelchairWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 mobility plus near meWeb1 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 … mobility plus of california