Edge domination in incidence graphs - Sam Adriaensen

Title: Edge domination in incidence graphs

Abstract: The edge domination number γ_e(G) of a graph G is the size of the smallest subset S of its edges, such that any edge in G intersects some edge of S. In this talk, we will discuss the edge domination number of incidence graphs of some nice incidence structures. In particular, the following result is central:

Theorem: Let G be the incidence graph of a symmetric 2 − (v, k, λ) design D. Then v − γ_e(G) equals the largest number α such that D contains a set X of α points and a set Y of α blocks, with no point of X incident with a block of Y . 

This leads us to explore upper and lower bounds on α in different incidence structures. 

We also investigate semi-biplanes, which are incidence structures that are close to being symmetric 2 − (v, k, 2) designs. We explore to which degree this theorem holds in semi-biplanes.

Joint work with Sam Spiro and Sam Mattheus