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 … 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 …
Did you know?
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 … 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.
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. 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
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 … 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 …
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 … church is a family not an eventWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 church is a hospitalWebRegular 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 … church is a hospital for the brokenWebThe 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 ... church is a hospital for sinnersWebThe 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 church is a group of peopleWebOther 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]. church is a communionWeb24 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 … dewalt 20v battery and charger deal