Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Journal of Combinato...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Journal of Combinatorial Theory Series B
Article
License: Elsevier Non-Commercial
Data sources: UnpayWall
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Journal of Combinatorial Theory Series B
Article . 1990
License: Elsevier Non-Commercial
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Journal of Combinatorial Theory Series B
Article . 1990 . Peer-reviewed
License: Elsevier Non-Commercial
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1990
Data sources: zbMATH Open
DBLP
Article
Data sources: DBLP
versions View all 5 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Intersection diagrams of distance-biregular graphs

Authors: Kazumasa Nomura;

Intersection diagrams of distance-biregular graphs

Abstract

Let G be a connected graph. For a fixed edge uv of G, put \(D^ i_ j=D^ i_ j(u,v)=\Gamma_ i(u)\cap \Gamma_ j(v).\) The family \(\{D^ i_ j\}_{i,j}\) is called the intersection diagram of G with respect to the edge uv. We have obtained several applications of intersection diagrams to distance-regular graphs. In this paper we apply the intersection diagrams to distance-biregular graphs to obtain the following results. Theorem 2. Let G be a distance-biregulr graph with girth \(g\equiv 0\) (mod 4). Let \(s+1\) and \(t+1\) be the valency of G and assume s and t are relatively prime. Then G is isomorphic to a generalized polygon. Theorem 3. Let G be a distance-biregular graph of girth \(g\equiv 0\) (mod 4). Assume G has the valency \(s+1\) and 3. Then one of the following two cases occurs: (1) G is a generalized polygon; (2) \(s=2^ h-2\) for some h with \(h\leq g/2\), \(d(G)\leq g/2+g/h\).

Related Organizations
Keywords

Computational Theory and Mathematics, generalized polygon, Association schemes, strongly regular graphs, Discrete Mathematics and Combinatorics, intersection diagram, distance-biregulr graph, Theoretical Computer Science

  • BIP!
    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).
    7
    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).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
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).
BIP!Citations provided by BIP!
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.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Average
Top 10%
Average
hybrid