Minimum Edge Cuts in Diameter 2 Graphs

Open access

Abstract

Plesnik proved that the edge connectivity and minimum degree are equal for diameter 2 graphs. We provide a streamlined proof of this fact and characterize the diameter 2 graphs with a nontrivial minimum edge cut.

[1] G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th Ed. (CRC Press, 2005).

[2] P. Erdős and R.J. Wilson, On the chromatic index of almost all graphs, J. Combin. Theory Ser. B 23 (1977) 255–257. doi:10.1016/0095-8956(77)90039-9

[3] J. Plesnik, Critical graphs of a given diameter, Acta Fac. Rerum Natur. Univ. Comenian. Math. 30 (1975) 71–93.

Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information


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CiteScore 2017: 0.64

SCImago Journal Rank (SJR) 2017: 0.633
Source Normalized Impact per Paper (SNIP) 2017: 1.095

Mathematical Citation Quotient (MCQ) 2017: 0.36

Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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