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A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

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 ...

Gradshteyn and Ryzhik (2000) define the circulant determinant by (1) where omega_j is the nth root of unity. The second-order circulant determinant is |x_1 x_2; x_2 ...

An n×n matrix whose rows are composed of cyclically shifted versions of a length-n list l. For example, the 4×4 circulant matrix on the list l={1,2,3,4} is given by C=[4 1 2 ...

A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs. The first few are ...

The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. ...

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

The n-Andrásfai graph is a circulant graph on 3n-1 nodes whose indices are given by the integers 1, ..., 3n-1 that are congruent to 1 (mod 3). The Andrásfai graphs have graph ...

Knuth (2008, p. 44) terms the 24-vertex graph based on the notes of the musical scale illustrated above the "musical graph." This graph can be seen to be the 24-vertex case ...