Quelle regprop.xml Sprache: XML

<Chapter Label="regprop">
<Heading>Regular graphs</Heading>

In this chapter we give functions used to identify graphs with various
regularity properties and determine their parameters.

<Section Label="Regular graphs">
<Heading>Regular graphs</Heading>

A graph <M>\Gamma</M> is <E>regular</E> with <E>parameters</E> <M>(v,k)</M>
if <M>\Gamma</M> is simple and undirected, it has order <M>v</M>,
and every vertex of <M>\Gamma</M> has degree <M>k</M>.

<#Include Label="RGParameters">

<#Include Label="IsRG">

<#Include Label="IsFeasibleRGParameters">

</Section>

<Section Label="Edge-regular graphs">
<Heading>Edge-regular graphs</Heading>

A graph <M>\Gamma</M> is <E>edge-regular</E> with <E>parameters</E>
<M>(v,k,a)</M> if it is regular with parameters <M>(v,k)</M>, it has at
least one edge, and every pair of adjacent vertices have exactly <M>a</M>
common neighbours.

<#Include Label="ERGParameters">

<#Include Label="IsERG">

<#Include Label="IsFeasibleERGParameters">

</Section>

<Section Label="Strongly regular graphs">
<Heading>Strongly regular graphs</Heading>

A graph <M>\Gamma</M> is <E>strongly regular</E> with <E>parameters</E>
<M>(v,k,a,b)</M> if it is edge-regular with parameters <M>(v,k,a)</M>,
it has at least one pair of distinct non-adjacent vertices, and every
pair of distinct non-adjacent vertices have exactly <M>b</M>
common neighbours.

<#Include Label="SRGParameters">

<#Include Label="IsSRG">

<#Include Label="IsFeasibleSRGParameters">

</Section>

</Chapter>

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