Strong (weak) edge-edge domination number of a graph

R. S. Bhat; S. S. Kamath; Surekha R. Bhat

Strong (weak) edge-edge domination number of a graph

R. S. Bhat^*, S. S. Kamath, Surekha R. Bhat

^*Corresponding author for this work

Department of Mathematics, Manipal Institute of Technology, Manipal

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

For any edge x=uv of an isolate free graph G(V,E),(N[x]) is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, e-dominates an edge y if y ∈ (N[x]). A set L ⊆ E is an Edge-Edge Dominating Set (EED-set) if every edge in E-L is e-dominated by an edge in L. The edge-edge domination number γ _ee(G) is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some known graph parameters.

Original language	English
Pages (from-to)	5525-5531
Number of pages	7
Journal	Applied Mathematical Sciences
Volume	6
Issue number	109-112
Publication status	Published - 16-10-2012

All Science Journal Classification (ASJC) codes

Applied Mathematics

Cite this

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N2 - For any edge x=uv of an isolate free graph G(V,E),(N[x]) is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, e-dominates an edge y if y ∈ (N[x]). A set L ⊆ E is an Edge-Edge Dominating Set (EED-set) if every edge in E-L is e-dominated by an edge in L. The edge-edge domination number γ ee(G) is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some known graph parameters.

AB - For any edge x=uv of an isolate free graph G(V,E),(N[x]) is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, e-dominates an edge y if y ∈ (N[x]). A set L ⊆ E is an Edge-Edge Dominating Set (EED-set) if every edge in E-L is e-dominated by an edge in L. The edge-edge domination number γ ee(G) is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some known graph parameters.

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ER -

Strong (weak) edge-edge domination number of a graph

Abstract

All Science Journal Classification (ASJC) codes

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