Abstract
For a graph G=V,E, a subset F of E is called an edge dominating set of G if every edge not in F is adjacent to some edge in F. The edge domination number γ′G of G is the minimum cardinality taken over all edge dominating sets of G. Here, we determine the edge domination number for shadow graphs, middle graphs, and total graphs of paths and cycles.
Highlights
The domination in graphs is one of the concepts in graph theory which has attracted many researchers to work on it because of its many and varied applications in such fields as linear algebra and optimization, design and analysis of communication networks, and social sciences and military surveillance
The set S ⊆ V of vertices in a graph G is called a dominating set if every vertex V ∈ V is either an element of S or is adjacent to an element of S
The middle graph of a connected graph G denoted by M(G) is the graph whose vertex set is V(G) ∪ E(G) where two vertices are adjacent if (i) they are adjacent edges of G, or (ii) one is a vertex of G and the other is an edge incident with it
Summary
The domination in graphs is one of the concepts in graph theory which has attracted many researchers to work on it because of its many and varied applications in such fields as linear algebra and optimization, design and analysis of communication networks, and social sciences and military surveillance. The present paper is focused on edge domination in graphs. The set S ⊆ V of vertices in a graph G is called a dominating set if every vertex V ∈ V is either an element of S or is adjacent to an element of S.
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