Events

DMS Combinatorics Seminar

Time: Oct 23, 2024 (02:00 PM)
Location: 328 Parker Hall

Details:

pavelescu

Speaker: Andrei Pavelescu  (University of South Alabama)

Title: Topological Properties of Graphs and Connected Domination

Abstract: The connected domination number γc(G) of G is the minimum cardinality of dominating sets S of G which induces a connected subgraph G[S] of G. We present some sharp bounds for γc(G), together with some open questions. We show how the connected domination can be used to establish results about topological properties of graphs and their complements. A graph G is called bi-knotlessly embeddable (bi-nIK), if both G and its complement, ¯G, admit an embedding in R3 with every cycle represented by a trivial knot. By size arguments, for large enough order n, the complete graph Kn cannot be bi-nIK. We are asking for the smallest order n, such that Kn is not bi-nIK. We prove that every graph of order 15 or more cannot be bi-nIK.