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 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 …

Signed k,k -domatic number of a graph - CORE

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]. 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 ... cty mtp entertainment

Fractional Domatic, Idomatic, and Total Domatic Numbers 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 surely … Web1 de jan. de 2024 · The fractional idiomatic and fractional total domatic numbers are defined analogously with all families \ (\mathcal {F}\) of independent dominating sets and … 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 easily.install foil dryer vent