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Weak roman domination in graphs

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Roushini Leely Pushpam P., Malini Mai T.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 1

161-170

Let G = (V,E) be a graph and f be a function f:V → {0,1,2}. A vertex u with f(u) = 0 is said to be undefended with respect to f, if it is not adjacent to a vertex with positive weight. The function f is a weak Roman dominating function (WRDF) if each vertex u with f(u) = 0 is adjacent to a vertex v with f(v) > 0 such that the function f': V → {0,1,2} defined by f'(u) = 1, f'(v) = f(v)-1 and f'(w) = f(w) if w ∈ V-{u,v}, has no undefended vertex. The weight of f is $w(f) = ∑_{v ∈ V}f(v)$. The weak Roman domination number, denoted by $γ_r(G)$, is the minimum weight of a WRDF in G. In this paper, we characterize the class of trees and split graphs for which $γ_r(G) = γ(G)$ and find $γ_r$-value for a caterpillar, a 2×n grid graph and a complete binary tree.

On super (a,d)-edge antimagic total labeling of certain families of graphs

100%

Roushini Leely Pushpam P., Saibulla A.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 3

535-543

A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f: V(G) ∪ E(G) → {1, 2,...,p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2,..., p} and the edge labels are {p + 1, p + 2,...,p + q}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Roushini Leely Pushpam P.

1 Malini Mai T.

1 Saibulla A.

1 2012

1 2011

Wyniki wyszukiwania

Weak roman domination in graphs

On super (a,d)-edge antimagic total labeling of certain families of graphs