Displaying similar documents to “Signed Roman Edgek-Domination in Graphs”

Signed Total Roman Edge Domination In Graphs

Leila Asgharsharghi, Seyed Mahmoud Sheikholeslami (2017)

Discussiones Mathematicae Graph Theory

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Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open neighborhood of e, and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e′ for which f(e′) = 2. The weight of a signed total Roman edge dominating function f is !(f) = Ʃe∈E f(e). The signed total Roman edge domination number...

On edge detour graphs

A.P. Santhakumaran, S. Athisayanathan (2010)

Discussiones Mathematicae Graph Theory

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For two vertices u and v in a graph G = (V,E), the detour distance D(u,v) is the length of a longest u-v path in G. A u-v path of length D(u,v) is called a u-v detour. A set S ⊆V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn₁(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn₁(G) is an edge detour basis of G. A connected graph G is called an edge detour graph if it has...

Total edge-domatic number of a graph

Bohdan Zelinka (1991)

Mathematica Bohemica

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The total edge-domatic number of a graph is introduced as an edge analogue of the total domatic number. Its values are studied for some special classes of graphs. The concept of totally edge-domatically full graph is introduced and investigated.