On the total domatic number of regular graphs
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 … Web× 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.
On the total domatic number of regular graphs
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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 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.
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 ... 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
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 … 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 …
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.
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. girl beatles lyrics meaningWebWe 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 … fun church christmas gamesWeb1 de out. de 2004 · 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 … girl beatles sheet musicWebWe 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 girl beatles guitar chordsWebG 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 ... girl beatles sheet music pianoWebh. 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]. … fun church games for all agesWebIn 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. girl beatles cover