Graph details
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Adjacency matrix[Too large to display] |
Adjacency list[Too large to display] |
HoG graph id
48173
Graph name
(5,5) cage
Graph submitted by
Sancuan Zhang
Invariant values
The definitions of the invariants can be found here.| Invariant | Value | Invariant | Value |
|---|---|---|---|
| Acyclic | No | Index | 5 |
| Algebraic Connectivity | 2.764 | Laplacian Largest Eigenvalue | 8.236 |
| Average Degree | 5 | Longest Induced Cycle | 14 |
| Bipartite | No | Longest Induced Path | 16 |
| Chromatic Index | Computation time out | Matching Number | 15 |
| Chromatic Number | 4 | Maximum Degree | 5 |
| Circumference | 30 | Minimum Degree | 5 |
| Claw-Free | No | Minimum Dominating Set | 7 |
| Clique Number | 2 | Number of Components | 1 |
| Connected | Yes | Number of Edges | 75 |
| Density | 0.172 | Number of Triangles | 0 |
| Diameter | 3 | Number of Vertices | 30 |
| Edge Connectivity | 5 | Planar | No |
| Eulerian | No | Radius | 3 |
| Genus | 9 | Regular | Yes |
| Girth | 5 | Second Largest Eigenvalue | 2.236 |
| Hamiltonian | Yes | Smallest Eigenvalue | -3.236 |
| Independence Number | 10 | Vertex Connectivity | 5 |
A table row rendered like this indicates that the graph is marked as being interesting for that invariant.
Comments
Posted by Sancuan Zhang at Jan 1, 2022 12:30 PM.
A 5-regular graph with girth 5 has at least 30 vertices; any graph attaining the minimum is called a (5,5) cage.
The graph has 30 automorphisms.
See the paper Exoo, G. , & Jajcay, R. . (2011). Dynamic cage survey. The Electronic Journal of Combinatorics electronic only. Link:https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS16/pdf
The graph has 30 automorphisms.
See the paper Exoo, G. , & Jajcay, R. . (2011). Dynamic cage survey. The Electronic Journal of Combinatorics electronic only. Link:https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS16/pdf
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