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A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

The Loupekine snarks are the two snarks on 22 vertices and 33 edges illustrated above. They are implemented in the Wolfram Language as GraphData["LoupekineSnark1"] and ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The flower snarks, denoted J_n for n=5, 7, 9, ..., are a family of graphs discovered by Isaacs (1975) which are snarks. The construction for flower snarks may be generalized ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

A 2-dimensional discrete percolation model is said to be mixed if both graph vertices and graph edges may be "blocked" from allowing fluid flow (i.e., closed in the sense of ...

Let N^* be the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored for any n>=N^*, a complete graph K_4 of one color with ...

The blossom algorithm (Edmonds 1965) finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for ...

Given a weighted, undirected graph G=(V,E) and a graphical partition of V into two sets A and B, the cut of G with respect to A and B is defined as cut(A,B)=sum_(i in A,j in ...