Co-Roman domination in trees
Subject Areas : Statistics
Rana Khoeilar
1
(
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz-Iran
)
Marzieh sorudi
2
(
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz-Iran
)
Keywords: تابع احاطهگر رومی, عدد احاطهای هم-رومی, تابع احاطهگر هم-رومی, عدد احاطهای رومی,
Abstract :
Abstract: Let G=(V,E) be a graph and let f:V(G)→{0,1,2} be a function. A vertex v is protected with respect to f, if f(v)>0 or f(v)=0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function, abbreviated CRDF if: (i) every vertex in V is protected, and (ii) each u∈V with positive weight has a neighbor v∈V with f(v)=0 such that the function f_uv:V→{0,1,2}, defined by f_uv (v)=1, f_uv (u)=f(u)-1 and f_uv (x)=f(x)for x∈V-\{v,u}, has no unprotected vertex. The weight of f is ω(f)=∑_(v∈V)▒〖f(v)〗. The co-Roman domination number of a graph G , denoted by γ_cr G), is the minimum weight of a co-Roman dominating function on G . In this paper, we first present an upper bound on the co-Roman domination number of trees in terms of order, the number of leaves and supports. Then we find bounds on the co-Roman domination number of a graph and its other dominating parameters .
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