Nonexistence of Graphs with Cyclic Defect

descriptionPublicationkeyboard_double_arrow_right Article 31 Mar 2011 Australia Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 18 (eissn: 1077-8926,

Copyright policy )

Authors: Miller, Mirka;

doi: 10.37236/558

handle: 1959.13/1064932

Nonexistence of Graphs with Cyclic Defect

- Summary
- Subjects
- Metrics

Abstract

In this note we consider graphs of maximum degree $\Delta$, diameter $D$ and order ${\rm M}(\Delta,D) - 2$, where ${\rm M}(\Delta,D)$ is the Moore bound, that is, graphs of defect 2. Delorme and Pineda-Villavicencio conjectured that such graphs do not exist for $D\geq 3$ if they have the so called 'cyclic defect'. Here we prove that this conjecture holds.

Country

Australia

Related Organizations

University of Newcastle Australia
Australia

Keywords

Extremal problems in graph theory, defect, graphs with cyclic defect, Moore bound, repeat, Structural characterization of families of graphs, Paths and cycles

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average