On the total domatic number of regular graphs
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 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 ...
On the total domatic number of regular graphs
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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 … 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 …
Webتعداد نشریات: 44: تعداد شمارهها: 1,460: تعداد مقالات: 11,915: تعداد مشاهده مقاله: 21,843,664: تعداد ... 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 …
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 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 …
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.
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 … cliff quality cleaningWeb20 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. cliff quay water recycling centreWebThe 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 … cliff quay sewage treatment worksWebThe 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. boat 12Web14 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 … boat 1200f sunburnWebIn 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 … cliff quackenbush a separate peaceWebIn 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 … boat 1200 f