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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Published in | Applied mathematics letters Vol. 24; no. 11; pp. 1933 - 1937 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Kidlington
Elsevier Ltd
01.11.2011
Elsevier |
Subjects | |
Online Access | Get full text |
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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
. |
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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 |