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On maximum induced matching numbers of special grids

Adefokun T. C., Ajayi D. O.

Journal of Mathematics and Applications

2018

Vol. 41

5--18

A subset M of the edge set of a graph G is an induced matching of G if given any two edges e1; e2 ∈ M, none of the vertices on e1 is adjacent to any of the vertices on e2. Suppose that Max(G), a positive integer, denotes the maximum size of M in G, then, M is the maximum induced matching of G and Max(G) is the maximum induced matching number of G. In this work, we obtain upper bounds for the maximum induced matching number of grid G = G n,m; n ≥ 9; m ≡ 3 mod 4; m ≥ 7, and nm odd.