On the total domatic number of regular graphs
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 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.
On the total domatic number of regular graphs
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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 … 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 …
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 ...
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 … 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 ...
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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]. high gaba symptomsWebalmost 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 … how ict support online collaborationWeb1 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 … high gain aerial cslWebThe 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 … high gain access pointWeb24 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 … how ict tools are being abusedWeb20 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. how i cured cancerWebclass 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 ... how i cured my ankylosing spondylitis