Thumbnail Image
Item

Regular graphs with maximal energy per vertex

van Dam,E.R.
; 
Haemers,W.H.
; 
Koolen,J.H.
Abstract
We study the energy per vertex in regular graphs. For every k⩾2, we give an upper bound for the energy per vertex of a k -regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs of projective planes of order k−1 or, in case k=2, the disjoint union of triangles and hexagons. For every k, we also construct k-regular subgraphs of incidence graphs of projective planes for which the energy per vertex is close to the upper bound. In this way, we show that this upper bound is asymptotically tight.
Description
Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Tilburg University Research Output Collection
Show all metadata
Files
Thumbnail Image
energypvpost.pdf
Adobe PDF, 291.48 KB
Research Projects
Organizational Units
Journal Issue
Keywords
Energy of graphs, eigenvalues of graphs, projective planes, elliptic semiplanes, cages
Citation
van Dam, E R, Haemers, W H & Koolen, J H 2014, 'Regular graphs with maximal energy per vertex', Journal of Combinatorial Theory Series B, vol. 107, no. July 2014, pp. 123-131. https://doi.org/10.1016/j.jctb.2014.02.007
URI
https://hdl.handle.net/20.500.14602/60594
Embedded videos