Vertex Count

Author

Eric W. Weisstein
June 30, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/VertexCount.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/VertexCount.html.

©2021 Wolfram Research, Inc. except for portions noted otherwise

Usage

?VertexCount

Parametrized families

GraphDataCountTable["VertexCount",{"LucasCube"->000032,"Pell"->000129,"Tetrahedral"->000292}]

Parametrized families

LucasCube

Munarini, E.; Perelli Cippo, C.; and Zagaglia Salvi, N.  "On the Lucas Cubes."  Fibonacci Quart. 39, 12–21, 2001.

https://www.fq.math.ca/Issues/39-1.pdf

seq=Table[GraphData[{"LucasCube",n},"VertexCount"],{n,15}]

FindSequenceFunction[seq,n]

Pell

A000129

seq=Table[GraphData[{"Pell",n},"VertexCount"],{n,0,9}]

FindSequenceFunction[seq,n+1]

Tetrahedral

l=Table[VertexCount[TetrahedralGraph[n]],{n,6,12}]

FindSequenceFunction[l,n-5]//Factor

Table[Binomial[n,3],{n,6,12}]

Test

Monitor[l={GraphData[g=#,"V"],VertexCount[GraphData[#]]}&/@GraphData[All],g];//Timing

Select[l,UnsameQ@@#&]