Geodesic
On the connectivity of Cartesian product of graphs
Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 293-297.

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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.
DOI : 10.26493/1855-3974.313.e10
Keywords: connectivity, Cartesian product 
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Jelena Govorčin; Riste Škrekovski. On the connectivity of Cartesian product of graphs. Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 293-297. doi : 10.26493/1855-3974.313.e10. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.313.e10/

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