THE DIAMETER AND RADIUS OF RADIALLY MAXIMAL GRAPHS
2021
A graph is called radially maximal if it is not complete and the addition of any new edge decreases its radius. In 1976 Harary and Thomassen proved that the radius $r$ and diameter $d$ of any radially maximal graph satisfy $r\le d\le 2r-2.$ Dutton, Medidi and Brigham rediscovered this result with a different proof in 1995 and they posed the conjecture that the converse is true, that is, if $r$ and $d$ are positive integers satisfying $r\le d\le 2r-2,$ then there exists a radially maximal graph with radius $r$ and diameter $d.$ We prove this conjecture and a little more.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
1
References
0
Citations
NaN
KQI