Weak signed Roman domination in graphs

Document Type : Original paper

Author

RWTH Aachen University

Abstract

A weak signed Roman dominating function (WSRDF) of a graph G with vertex set V(G) is defined as a function f:V(G)→{−1,1,2} having the property that ∑x∈N[v]f(x)≥1 for each v∈V(G), where N[v] is the closed neighborhood of v. The weight of a WSRDF is the sum of its function values over all vertices. The weak signed Roman domination number of G, denoted by γwsR(G), is the minimum weight of a WSRDF in G. We initiate the study of the weak signed Roman domination number, and we present different sharp bounds on γwsR(G). In addition, we determine the weak signed Roman domination number of some classes of graphs.

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References

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Communications in Combinatorics and Optimization
Volume 5, Issue 2
December 2020
Pages 111-123

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