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The Faulkner-Younger graphs (Faulkner and Younger 1974) are the cubic polyhedral nonhamiltonian graphs on 42 and 44 vertices illustrated above that are counterexamples to ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

The Janko-Kharaghani graphs are two strongly regular graph on 936 and 1800 vertices. They have regular parameters (nu,k,lambda,mu)=(936,375,150,150) and (1800,1029,588,588), ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018). Two 13- and 15-node graphs, denoted alpha and beta respectively, were used ...

The Royle graphs are the two unique simple graphs on eight nodes whose sigma polynomials have nonreal roots (Read and Wilson 1998, p. 265). The sigma polynomials of these ...

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic ...