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The Hall graph is a distance-transitive graph on 65 vertices having intersection array {10,6,4,1;1,2,5} (Hall 1980). It is denoted Gamma^((3)) by Hall (1980) and was ...

A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

Define a = d(u,v)d(w,x) (1) b = d(u,w)d(v,x) (2) c = d(u,x)d(v,w), (3) where u, v, w, and x are vertices of a graph and d(i,j) is the graph distance between vertices i and j. ...

A uniquely pancyclic graph is a graph that has exactly one cycle of each length between 3 and the graph's vertex count. Uniquely pancyclic graphs are therefore a special case ...

A string or word is said to be admissible if that word appears in a given sequence. For example, in the sequence aabaabaabaabaab..., a, aa, baab are all admissible, but bb is ...

A set (usually of letters) from which a subset is drawn. A sequence of letters is called a word, and a set of words is called a code.

The number of empty neighbors of a cluster.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.