Monotonicity of the order of ( D ; g ) -cages

A ( D ; g ) -cage is a graph having degree set D , girth g , and the minimum possible number of vertices, which is denoted by n ( D ; g ) . When D = { r } the corresponding ( { r } ; g ) -cage is clearly r -regular, and is called an ( r ; g ) -cage. In this work we prove that if g < g ′ then n (...

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Bibliographic Details
Published inApplied mathematics letters Vol. 24; no. 11; pp. 1933 - 1937
Main Authors Balbuena, C., Marcote, X.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.11.2011
Elsevier
Subjects
Cage
Degree set
Exact sciences and technology
Girth
Graphs
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Degree set
Girth
Cage
Graph degree
Applied mathematics
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Summary:A ( D ; g ) -cage is a graph having degree set D , girth g , and the minimum possible number of vertices, which is denoted by n ( D ; g ) . When D = { r } the corresponding ( { r } ; g ) -cage is clearly r -regular, and is called an ( r ; g ) -cage. In this work we prove that if g < g ′ then n ( D ; g ) < n ( D ; g ′ ) under certain requirements on the elements of the degree set D or on the girth g .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2011.05.024