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- Title
On the Signed strong total Roman domination number of graphs.
- Authors
Mahmoodi, A.; Atapour, M.; Norouzian, S.
- Abstract
Let G = (V,E) be a finite and simple graph of order n and maximum degree. A signed strong total Roman dominating function on a graph G is a function f: V (G) {-1, 1, 2, 2 + 1} satisfying the condition that (i) for every vertex v of G, f(N(v)) = S uN(v) f(u) = 1, where N(v) is the open neighborhood of v and (ii) every vertex v for which f(v) = -1 is adjacent to at least one vertex w for which f(w) = 1 + 1 2 |N(w) n V-1| where V-1 = {vV: f(v) = -1}. The minimum of the values(f) = S vV f(v), taken over all signed strong total Roman dominating functions f of G, is called the signed strong total Roman domination number of G and is denoted by ssTR(G). In this paper, we initiate signed strong total Roman domination number of a graph and give several bounds for this parameter. Then, among other results, we determine the signed strong total Roman domination number of special classes of graphs.
- Subjects
ROMAN numerals; GRAPH theory; GEOMETRIC vertices; MATHEMATICAL bounds; PARAMETER estimation
- Publication
Tamkang Journal of Mathematics, 2023, Vol 54, Issue 3, p265
- ISSN
0049-2930
- Publication type
Article
- DOI
10.5556/j.tkjm.54.2023.3907