Contract graph sponsor: VEGA; Contract grant number: 1/0781/11; Contract grant sponsor: APVV; Contract grant number: 0223-10; Contract grant sponsor: APVV-EUROCORES Programme EUROGIGA, project GREGAS; Contract grant number ESF-EC-0009-10.
Smallest Vertex-Transitive Graphs of Given Degree and Diameter
Article first published online: 31 JAN 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 2, pages 137–149, February 2014
How to Cite
Knor, M. and Širáň, J. (2014), Smallest Vertex-Transitive Graphs of Given Degree and Diameter. J. Graph Theory, 75: 137–149. doi: 10.1002/jgt.21727
- Issue published online: 2 DEC 2013
- Article first published online: 31 JAN 2013
- Manuscript Revised: 23 DEC 2012
- Manuscript Received: 7 MAR 2012
- VEGA. Grant Number: 1/0781/11
- APVV. Grant Number: 0223-10
- APVV-EUROCORES Programme EUROGIGA. Grant Number: ESF-EC-0009-10
- extremal problem;
- degree/diameter problem;
- vertex-transitive graph;
- Cayley graph;
- smallest graph
For every d and k, we determine the smallest order of a vertex-transitive graph of degree d and diameter k, and in each such case we show that this order is achieved by a Cayley graph.