On the total domatic number of regular graphs

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August undefined, 2024

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 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.

CUBIC GRAPHSWITH TOTAL DOMATIC NUMBER AT LEAST TWO

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 … 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 … can soy formula cause constipation in babies

On the total domatic number of regular graphs - ResearchGate

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. 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 … 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. can soy lecithin cause gas

On the total domatic number of regular graphs - Semantic Scholar

CubicGraphswithTotalDomaticNumberatLeastTwo - arXiv

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 … 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 can soy make you gain weightWebnumber 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 … flared nesting band with diamonds

"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 " - On the total domatic number of regular graphs

On the total domatic number of regular graphs

On the signed total domatic number of a graph Request PDF

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 …

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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. 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} }

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 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 …

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 … Webتعداد نشریات: 44: تعداد شماره‌ها: 1,460: تعداد مقالات: 11,915: تعداد مشاهده مقاله: 21,843,664: تعداد ...

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].

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 … can soy lecithin affect the thyroidWebIn 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 … flared mouwen topWebgraphs. 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. can soy lower testosteroneWeb1 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 … can soy milk cause breast painWeb14 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 … can soy milk make men grow breastWeb28 de jun. de 2011 · Semantic Scholar's Logo can soy lecithin cause allergiesWeb1 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 … flared overpants crossword