On the connectivity of Cartesian product of graphs

Jelena Govorčin, Riste Škrekovski


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.


connectivity, Cartesian product

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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications