Graph details

Graph # 502

Adjacency matrix

00000001
00000100
00000010
00000010
00000100
01001001
00110001
10000110

Adjacency list

1: 8
2: 6
3: 7
4: 7
5: 6
6: 2 5 8
7: 3 4 8
8: 1 6 7

HoG graph id

502

Graph name

n/a

Graph submitted by

GraPHedron

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic Yes Index 2.136
Algebraic Connectivity 0.268 Laplacian Largest Eigenvalue 4.814
Average Degree 1.75 Longest Induced Cycle undefined
Bipartite Yes Longest Induced Path 4
Chromatic Index 3 Matching Number 3
Chromatic Number 2 Maximum Degree 3
Circumference undefined Minimum Degree 1
Claw-Free No Minimum Dominating Set 3
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 7
Density 0.25 Number of Triangles 0
Diameter 4 Number of Vertices 8
Edge Connectivity 1 Planar Yes
Eulerian No Radius 2
Genus 0 Regular No
Girth undefined Second Largest Eigenvalue 1.414
Hamiltonian No Smallest Eigenvalue -2.136
Independence Number 5 Vertex Connectivity 1

A table row rendered like this indicates that the graph is marked as being interesting for that invariant.

Comments

Posted by GraPHedron at Mar 28, 2012 11:56 AM.
Is an extremal graph found by GraPHedron. See "H. Melot, Facet defining inequalities among graph invariants: the system graphedron. Discrete Applied Mathematics 156 (2008), 1875-1891" for more information.

Posted by Kevin Ryde at Jan 31, 2016 7:20 AM.
OEIS A179016 and related sequences give a "binary beanstalk" where each vertex is an integer n with edge to parent n-CountOneBits(n). The graph here is the first 5 tree rows, being vertices n=0 to n=7 inclusive.
http://oeis.org/A179016/a179016.png

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