﻿ Weak signed Roman domination in graphs

# Weak signed Roman domination in graphs

##### چکیده

A {em weak signed Roman dominating function} (WSRDF) of a graph \$G\$ with vertex set \$V(G)\$ is defined as afunction \$f:V(G)rightarrow{-1,1,2}\$ having the property that \$sum_{xin N[v]}f(x)ge 1\$ for each \$vin V(G)\$, where \$N[v]\$ is theclosed 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 \$gamma_{wsR}(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 \$gamma_{wsR}(G)\$.In addition, we determine the weak signed Roman domination number of some classes of graphs.

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عنوان ژورنال:

دوره 5  شماره 2

صفحات  111- 123

تاریخ انتشار 2020-12-01

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