Can anyone explain the definition of the domination Induced matching (DIM) graph by figures to me? I know that a domination Induced matching graph of G is an induced matching that dominates every edge of G, but I can't imagine this. Thanks.
2026-03-30 00:15:18.1774829718
difference between matching graph and induced matching graph
192 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
I hope it can help you
A matching M of G is a dominating induced matching (say a DIM) of G if every edge of G is either in M or has a common end-vertex with exactly one edge in M. A DIM is also called an efficient edge domination set.
Not all graphs have a DIM, for instance the cycle with four vertices C4 has no DIM. The DIM problem asks whether a given graph has a dominating induced matching.
A graph with a DIM $M = \{12,34,56,78\}$.
On the dominating induced matching problem: Spectral results and sharp bounds