Relating hypergraph parameters of generalized power graphs

Speaker: Lucas L. S. Portugal, IME-UFF.

Date: 29 jul 2020, 16h.

Place: Google Meet:

Abstract: Graph parameters like the chromatic number, independence number, clique number and many others alongside with their corresponding adjacency matrix have been broadly studied and extended to hypergraphs classes. A generalized power graph $G^k_s$ of a graph $G$ is $k$-uniform hypergraph constructed by blowing up each vertex of $G$ into a $s$-set of vertices and then adding $k-2s$ vertices of degree one to each edge, where $k\geq 2s$. A natural question is whether there exists any relation between structural parameters and spectral parameters of $G^k_s$ with the respective parameters of the original graph $G$. In this paper we positively answer this question and investigate the parameters behavior.

Obs.: This joint work with Renata Del Vecchio (IME/UFF) and Simone Dantas (IME/UFF), was accepted for presentation and publication in the CTW 2020 (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization).