Abstract. Let γ(G) and γ'(G) be the domination number and edge domination number, respectively. The lexicographical Product G₁•G₂ of graph of G₁ and G₂ has vertex set V(G₁ • G₂)=V(G₁) × V(G₂) and edge set

E(G₁ • G₂)={(u₁v₁)(u₂v₂) | [u₁u₂ ∈ E(G₁)]∪[u₁=u₂ and v₁v₂ ∈ E(G₂)]}. In this paper, we determined generalization of domination and edge domination number on lexicographical product of complete graphs and any simple graph.

Received: February 9, 2013

AMS Subject Classification: 05C69, 05C70, 05C76

Key Words and Phrases: lexicographical product, domination number, edge domination number

Download paper from here.

---

DOI: 10.12732/ijpam.v85i4.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 4

---