Open AccessEdge dominating graph of a graph
Author(s) -
B. Basavanagoud,
Sunilkumar M. Hosamani
Publication year - 2013
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.43.2012.806
Subject(s) - combinatorics , mathematics , dominating set , vertex (graph theory) , graph , bound graph , discrete mathematics , complement graph , line graph , graph power
The edge dominating graph $E_{D}(G)$ of a graph $G=(V,E)$ is a graph with $V(E_{D}(G))=E(G)\cup S(G)$, where $S(G)$ is the set of all minimal edge dominating sets of $G$ with two vertices $u,v\in V(E_{D}(G))$ adjacent if $u\in E$ and $v$ is a minimal edge dominating set of $G$ containing $u$. In this paper, we establish the bounds on order and size, diameter and vertex(edge)connectivity