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The Brinkmann graph (misspelled by Cancela et al. (2004) as "Brinkman") is a weakly regular quartic graph on 21 vertices and 42 edges. It was first mentioned in Brinkmann ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...