Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2011

Graphs with four boundary vertices

Résumé

A vertex v of a graph G is a boundary vertex if there exists a vertex u such that the distance in G from u to v is at least the distance from u to any neighbour of v. We give a full description of all graphs that have exactly four boundary vertices, which answers a question of Hasegawa and Saito. To this end, we introduce the concept of frame of a graph. It allows us to construct, for every positive integer b and every possible ``distance-vector'' between b points, a graph G with exactly b boundary vertices such that every graph with b boundary vertices and the same distance-vector between them is an induced subgraph of G.

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hal-00558913 , version 1 (24-01-2011)

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  • HAL Id : hal-00558913 , version 1

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Tobias Müller, Attila Pór, Jean-Sébastien Sereni. Graphs with four boundary vertices. The Electronic Journal of Combinatorics, 2011, 18 (1), pp.P11. ⟨hal-00558913⟩
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