Abstract | ||
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A total k-rainbow dominating function (TkRDF) of G is a function f from the vertex set V(G) to the set of all subsets of the set {1, ..., k} such that (i) for any vertex v is an element of V(G) with f(v) = empty set the condition boolean OR(u is an element of N(v)) f(u) = {1, ..., k} is fulfilled, where N(v) is the open neighborhood of v, and (ii) the subgraph of G induced by {v is an element of V(G) vertical bar f(v) not equal empty set} has no isolated vertex. The total k-rainbow domination number, gamma(trk)(G), is the minimum weight of a TkRDF on G. The total k-rainbow domination subdivision number sd(gamma trk)(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total k-rainbow domination number. In this paper, we initiate the study of total k-rainbow domination subdivision number in graphs and we present sharp bounds for sd(gamma trk)(G). In addition, we determine the total 2-rainbow domination subdivision number of complete bipartite graphs and show that the total 2-rainbow domination subdivision number can be arbitrary large. |
Year | Venue | Keywords |
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2020 | COMPUTER SCIENCE JOURNAL OF MOLDOVA | total k-rainbow domination, total k-rainbow domination subdivision number, k-rainbow domination |
DocType | Volume | Issue |
Journal | 28 | 2 |
ISSN | Citations | PageRank |
1561-4042 | 0 | 0.34 |
References | Authors | |
0 | 4 |
Name | Order | Citations | PageRank |
---|---|---|---|
R. Khoeilar | 1 | 12 | 6.57 |
Mahla Kheibari | 2 | 0 | 0.68 |
Zehui Shao | 3 | 119 | 30.98 |
Seyed Mahmoud Sheikholeslami | 4 | 54 | 28.15 |