Signed total Roman domination in graphs

Lutz Volkmann ()
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Lutz Volkmann: RWTH Aachen University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 3, No 13, 855-871

Abstract: Abstract Let $$G$$ G be a finite and simple graph with vertex set $$V(G)$$ V ( G ) . A signed total Roman dominating function (STRDF) on a graph $$G$$ G is a function $$f:V(G)\rightarrow \{-1,1,2\}$$ f : V ( G ) → { - 1 , 1 , 2 } satisfying the conditions that (i) $$\sum _{x\in N(v)}f(x)\ge 1$$ ∑ x ∈ N ( v ) f ( x ) ≥ 1 for each vertex $$v\in V(G)$$ v ∈ V ( G ) , where $$N(v)$$ N ( v ) is the neighborhood of $$v$$ v , and (ii) every vertex $$u$$ u for which $$f(u)=-1$$ f ( u ) = - 1 is adjacent to at least one vertex $$v$$ v for which $$f(v)=2$$ f ( v ) = 2 . The weight of an SRTDF $$f$$ f is $$\sum _{v\in V(G)}f(v)$$ ∑ v ∈ V ( G ) f ( v ) . The signed total Roman domination number $$\gamma _{stR}(G)$$ γ s t R ( G ) of $$G$$ G is the minimum weight of an STRDF on $$G$$ G . In this paper we initiate the study of the signed total Roman domination number of graphs, and we present different bounds on $$\gamma _{stR}(G)$$ γ s t R ( G ) . In addition, we determine the signed total Roman domination number of some classes of graphs.

Keywords: Signed total Roman dominating function; Signed total Roman domination number; Total dominating set; Total domination number; 05C69 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-015-9906-6

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