Excess
المؤلف:
Biggs, N. L. and Ito, T.
المصدر:
"Graphs with Even Girth and Small Excess." Math. Proc. Cambridge Philos. Soc. 88
الجزء والصفحة:
...
20-2-2021
1551
Excess
The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient.
In graph theory, excess refers to the quantity
 |
(1)
|
for a 
-regular graph 
on 
nodes with girth 
, where
![n_l(v,g)=<span style=]() {(v(v-1)^((g-1)/2)-2)/(v-2) for g odd; (2(v-1)^(g/2)-2)/(v-2) for g even " src="https://mathworld.wolfram.com/images/equations/Excess/NumberedEquation2.gif" style="height:86px; width:249px" /> |
(2)
|
(Biggs and Ito 1980, Wong 1982). A 
-cage graph having 
vertices (i.e., the minimal number, so that the excess is 
) is called a Moore graph.
REFERENCES:
Biggs, N. L. and Ito, T. "Graphs with Even Girth and Small Excess." Math. Proc. Cambridge Philos. Soc. 88, 1-10, 1980.
Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.
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