TY - JOUR

T1 - Dominating sets in finite generalized quadrangles

AU - Hernandez Lucas, Lisa

AU - Héger, Tamás

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85097167560&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.2106.423

DO - 10.26493/1855-3974.2106.423

M3 - Article

VL - 19

SP - 61

EP - 76

JO - Mathematica Contemporanea

JF - Mathematica Contemporanea

SN - 2317-6636

IS - 1

ER -