Graph details

Graph # 35455

Adjacency matrix

00001100
00001100
00000011
00000011
11000010
11000001
00111000
00110100

Adjacency list

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

HoG graph id

35455

Graph name

two 4-cycles cross-connected at 2 opposing vertices

Graph submitted by

Kevin Ryde

Invariant values

The definitions of the invariants can be found here.
Invariant Value Invariant Value
Acyclic No Index 2.562
Algebraic Connectivity 0.764 Laplacian Largest Eigenvalue 5.236
Average Degree 2.5 Longest Induced Cycle 6
Bipartite Yes Longest Induced Path 4
Chromatic Index 3 Matching Number 4
Chromatic Number 2 Maximum Degree 3
Circumference 6 Minimum Degree 2
Claw-Free No Minimum Dominating Set 2
Clique Number 2 Number of Components 1
Connected Yes Number of Edges 10
Density 0.357 Number of Triangles 0
Diameter 3 Number of Vertices 8
Edge Connectivity 2 Planar Yes
Eulerian No Radius 3
Genus 0 Regular No
Girth 4 Second Largest Eigenvalue 1.562
Hamiltonian No Smallest Eigenvalue -2.562
Independence Number 4 Vertex Connectivity 2

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

Comments

Posted by Kevin Ryde at Jun 14, 2020 11:21 AM.
Binomial both order 3. A "binomial both" order k is a binomial tree order k both up and down. Each vertex is an integer 0 to 2^k-1 written with k many bits. Each v>0 has an edge to v with its lowest 1-bit cleared (binomial tree parent). Each v<2^k-1 has an edge to v with its lowest 0-bit set to 1, which is a bit-flipped binomial tree. The result is a graded lattice. Here the global minimum (v=0) is one of the degree 3s, and the global maximum (v=7) the most-distant degree 3.

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