On the total domatic number of regular graphs

Author: nrxf

August undefined, 2024

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. 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 …

The Numerical Invariants concerning the Total Domination for …

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 … WebThe concept of domatic number and total domatic number was introduced by Cockayne etal.,in[10]and[9]respectively,andinvestigatedfurtherin[1,2,5,8,12,18,24,26,32,33]. In [33], Zelinka have shown the existence of graphs with very large minimum degree have a total domatic number 1. Chen et al., [8] and Goddard and Henning [12] have studied imdb terribly happy

The total { k }-domatic number of a graph - Springer

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 … Web11 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 … 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 … list of missouri vehicle inspection stations

On the (h,k)-domination numbers of iterated line digraphs

Approximating the Domatic Number - Rutgers University

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 … 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]. … imdb terence morganWebThe 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 … list of miss rheingold winners

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On the total domatic number of regular graphs

The total { k }-domatic number of a graph - Springer

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. 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].

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Web24 de mar. de 2024 · Domatic Number. Download Wolfram Notebook. The maximum number of disjoint dominating sets in a domatic partition of a graph is called its … 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.

Webgraphs. 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. 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 …

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 … Web1 de jan. de 2024 · The fractional idiomatic and fractional total domatic numbers are defined analogously with all families \ (\mathcal {F}\) of independent dominating sets and …

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

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 ... list of missouri non-profitsWebnumber 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 … list of missouri cities by populationWebCiteSeerX - 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 … imdb terry bradshaw wikipediaWebThe 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 ... list of miss pennsylvania winnersWeb1 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} } imdb tessa thompsonWebWe 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 … imdb tethered imdb texas chainsaw