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Dominating sets in finite generalized quadrangles

Journal Contribution - Journal Article

A dominating set in a graph is a set of vertices such that each vertex not in the set has a neighbor in the set. The domination number is the smallest size of a dominating set. We consider this problem in the incidence graph of a generalized quadrangle. We show that the domination number of a generalized quadrangle with parameters s and t is at most 2st+1, and we prove that this bound is sharp if s = t or if s = q - 1 and t = q + 1. Moreover, we give a complete classification of smallest dominating sets in generalized quadrangles where s = t, and give some general results for small dominating sets in the general case.

Journal: Ars Mathematica Contemporanea
ISSN: 2317-6636
Issue: 1
Volume: 19
Pages: 61-76
Number of pages: 16
Publication year:2020