# Graphs of diameter 3 with the minimum number of edges

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

The graph G is called a porcupine, if G{divides}A is a complete graph for some set A, every other vertex has degree one, and its only edge is joined to A. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that if G is a graph on n vertices of diameter 3 with maximum degree D, D > 2.31 {Mathematical expression}, D ≠ (n - 1)/2 and it has the mimimum number of edges, then it is a porcupine.

Original language English 333-337 5 Graphs and Combinatorics 6 4 https://doi.org/10.1007/BF01787701 Published - Dec 1990

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Vertex Degree
Graph in graph theory
Maximum Degree
Complete Graph
Divides

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Mathematics(all)

### Cite this

In: Graphs and Combinatorics, Vol. 6, No. 4, 12.1990, p. 333-337.

Research output: Contribution to journalArticle

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