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Maverick Graph

A maverick graph is a connected graph with smallest graph eigenvalue lambda_(min) satisfying -lambda^*<lambda_(min)<-2 that is not an augmented path extension of any rooted graph (Acharya and Jiang 2024). Here rho=1.32471... (OEIS A060006) is the plastic constant and

lambda^*=rho^(1/2)+rho^(-1/2)
(1)
=2.01980...
(2)

(OEIS A372244).

MaverickGraphs9

There are a total of 4752 maverick graphs, and the numbers of such graphs on n=9, ..., 19 vertices are 13, 629, 1304, 1237, 775, 408, 221, 107, 42, 13, 3 (OEIS A372243; Acharya and Jiang 2024). The 13 maverick graphs on 9 vertices are illustrated above. The 629 maverick graphs on 10 vertices include the (5,5)-tadpole graph, 9-pan graph, and (3,5,3)-kayak paddle graph.

See also

Graph Eigenvalue, Plastic Constant

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References

Acharya, H. and Jiang, Z. "Beyond the Classification Theorem of Cameron, Goethals, Seidel, and Shult." 19 Apr 2024. https://arxiv.org/abs/2404.13136.House of Graphs. Maverick Graphs. The (9,1)-Tadpole Graph, Spider S(4,3,1), and Kayak Paddle Graph KP(3,5,4).Sloane, N. J. A. Sequences A060006, A372243, and A372244 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Maverick Graph

Cite this as:

Weisstein, Eric W. "Maverick Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MaverickGraph.html

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