On the total domatic number of regular graphs

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

Domination in Cubic Graphs SpringerLink

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 … 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 ... fit watch walmart https://dalpinesolutions.com

The total { k }-domatic number of a graph - Springer

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 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 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. can i give my dog beano for gas

Signed total domatic number of a graph SpringerLink

Category:Fractional Domatic, Idomatic, and Total Domatic Numbers of a Graph

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On the total domatic number of regular graphs

The Numerical Invariants concerning the Total Domination for …

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 … 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].

On the total domatic number of regular graphs

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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 …

Web1 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 … http://www.math.clemson.edu/~calkin/Papers/calkin_dankelmann.pdf

Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 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

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 …

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 … can i give my dog benefiber for constipationWeb28 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 … fit watch reviewsWebThe 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 … fit water bottleWebThe 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. can i give my dog benadryl for licking pawsWeb19 de mar. de 2024 · In this paper, we show that for two non-trivial graphs $G$ and $H$, the domatic and total domatic numbers of their Cartesian product $G \cart H$ is … fit water bottle amazonWebalmost 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 … fit watch with music storageWebIn 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 … can i give my dog black walnut