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The disdyakis triacontahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

The Gewirtz graph, sometimes also called the Sims-Gewirtz graph (Brouwer), is an integral graph on 56 nodes and 280 edges that is also a regular graph of order 10. It is ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

A block graph, also called a clique tree, is a simple graph in which every block is a complete graph. The numbers of connected block graphs on n=1, 2, ... vertices are 1, 1, ...

The Reye graph is the transposition graph G_4 of order 4.

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

The Wells graph, sometimes also called the Armanios-Wells graph, is a quintic graph on 32 nodes and 80 edges that is the unique distance-regular graph with intersection array ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

"The" Sylvester graph is a quintic graph on 36 nodes and 90 edges that is the unique distance-regular graph with intersection array {5,4,2;1,1,4} (Brouwer et al. 1989, ...