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Meredith graph

4-regular undirected graph with 70 vertices and 140 edges

Field	Value
name	Meredith graph
image	[[Image:Meredith graph.svg	220px]]
image_caption	The Meredith graph
namesake	G. H. Meredith
vertices	70
edges	140
girth	4
diameter	8
radius	7
automorphisms	38698352640
chromatic_number	3
chromatic_index	5
properties	Eulerian
book thickness	3	queue number=2

In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973.

The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-Hamiltonian. It has book thickness 3 and queue number 2.

Published in 1973, it provides a counterexample to the Crispin Nash-Williams conjecture that every 4-regular 4-vertex-connected graph is Hamiltonian.{{cite journal

The characteristic polynomial of the Meredith graph is (x-4) (x-1)^{10} x^{21} (x+1)^{11} (x+3) (x^2-13) (x^6-26 x^4+3 x^3+169 x^2-39 x-45)^4.

Gallery

Image:Meredith graph 3COL.svg|The chromatic number of the Meredith graph is 3. Image:Meredith graph 5color edge.svg|The chromatic index of the Meredith graph is 5.

References

"Meredith graph".
Bondy, J. A. and Murty, U. S. R. "Graph Theory". Springer, p. 470, 2007.
Jessica Wolz, ''Engineering Linear Layouts with SAT''. Master Thesis, University of Tübingen, 2018
Bondy, J. A. and Murty, U. S. R. "Graph Theory with Applications". New York: North Holland, p. 239, 1976.
Tutte, W.T., ed., Recent Progress in Combinatorics. Academic Press, New York, 1969.

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