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Harries-Wong Graph


HarriesWongGraph

The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph.

The Harries-Wong graph is Hamiltonian with 94656 Hamiltonian cycles. It has 3288 distinct LCF notations, all of order 1, and one of which is given by [9, 25, 31, -17, 17, 33, 9, -29, -15, -9, 9, 25, -25, 29, 17, -9, 9, -27, 35, -9, 9, -17, 21, 27, -29, -9, -25, 13, 19, -9, -33, -17, 19, -31, 27, 11, -25, 29, -33, 13, -13, 21, -29, -21, 25, 9, -11, -19, 29, 9, -27, -19, -13, -35, -9, 9, 17, 25, -9, 9, 27, -27, -21, 15, -9, 29, -29, 33, -9, -25].

HarriesWongGraphMatrices

The plots above show the adjacency matrix, incidence matrix, and graph distance matrix for the Harries-Wong graph.

The Harries-Wong graph are cospectral graphs, meaning neither is determined by spectrum.

The following table summarizes properties of the Harries-Wong graph.

automorphism group order24
characteristic polynomial(x-3)(x-1)^4(x+1)^4(x+3)(x^2-6)(x^2-2)(x^4-6x^2+2)^5(x^4-6x^2+3)^4(x^4-6x^2+6)^5
chromatic number2
claw-freeno
clique number2
cospectral graph namesHarries graph
determined by spectrumno
diameter6
distance-regular graphno
edge chromatic number3
edge connectivity3
edge count105
Eulerianno
girth10
Hamiltonianyes
Hamiltonian cycle count94656
integral graphno
independence number35
perfect matching graphno
planarno
polyhedral graphno
radius6
regularyes
square-freeyes
traceableyes
triangle-freeyes
vertex connectivity3
vertex count70
weakly regular parameters(70,(3),(0),(0,1))

See also

Balaban 10-Cage, Cage Graph, Cospectral Graphs, Determined by Spectrum, Harries Graph

Explore with Wolfram|Alpha

References

Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. http://citeseer.ist.psu.edu/448980.html.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 272, 1998.Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.

Cite this as:

Weisstein, Eric W. "Harries-Wong Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Harries-WongGraph.html

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