On the connectivity of Cartesian product of graphs

Authors

  • Jelena Govorčin
  • Riste Škrekovski University of Ljubljana

DOI:

https://doi.org/10.26493/1855-3974.313.e10

Keywords:

connectivity, Cartesian product

Abstract

We give a new alternative proof of Liouville’s formula which states that for any graphs G and H on at least two vertices, κ(G □ H) = min{κ(G)|H|,  |G|κ(H),  δ(G) + δ(H)}, where κ and δ denote the connectivity number and minimum degree of a given graph, respectively. The main idea of our proof is based on construction of a vertex-fan which connects a vertex from V(G □ H) to a subgraph of G □ H. We also discuss the edge version of this problem as well as formula for products with more than two factors.

Published

2013-04-20

Issue

Section

Articles