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Distance-regularised graphs are distance-regular or distance-biregular

Distance-regularised graphs are distance-regular or distance-biregular
Distance-regularised graphs are distance-regular or distance-biregular
One problem with the theory of distance-regular graphs is that it does not apply directly to the graphs of generalised polygons. In this paper we overcome this difficulty by introducing the class of distance-regularised graphs, a natural common generalisation. These graphs are shown to either be distance-regular or fall into a family of bipartite graphs called distance-biregular. This family includes the generalised polygons and other interesting graphs. Despite this increased generality we are also able to extend much of the basic theory of distance-regular graphs to our wider class of graphs.
0095-8956
14-24
Godsil, C.
94db18f5-c157-40eb-a1b1-f07f1259bb73
Shawe-Taylor, J.
c32d0ee4-b422-491f-8c28-78663851d6db
Godsil, C.
94db18f5-c157-40eb-a1b1-f07f1259bb73
Shawe-Taylor, J.
c32d0ee4-b422-491f-8c28-78663851d6db

Godsil, C. and Shawe-Taylor, J. (1987) Distance-regularised graphs are distance-regular or distance-biregular. Journal of Combinatorial Theory, Series B, 43 (1), 14-24. (doi:10.1016/0095-8956(87)90027-X).

Record type: Article

Abstract

One problem with the theory of distance-regular graphs is that it does not apply directly to the graphs of generalised polygons. In this paper we overcome this difficulty by introducing the class of distance-regularised graphs, a natural common generalisation. These graphs are shown to either be distance-regular or fall into a family of bipartite graphs called distance-biregular. This family includes the generalised polygons and other interesting graphs. Despite this increased generality we are also able to extend much of the basic theory of distance-regular graphs to our wider class of graphs.

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Published date: August 1987
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 259848
URI: https://eprints.soton.ac.uk/id/eprint/259848
ISSN: 0095-8956
PURE UUID: ce417b9e-dbc2-4dcb-aff0-55cc5c418740

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Date deposited: 26 Aug 2004
Last modified: 15 Nov 2018 17:31

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