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A Haar graph H(n) is a bipartite regular indexed by a positive integer and obtained by a simple binary encoding of cyclically adjacent vertices. Haar graphs may be connected ...

The Grassmann graph J_q(n,k) is defined such that the vertices are the k-dimensional subspaces of an n-dimensional finite field of order q and edges correspond to pairs of ...

A bicubic nonhamiltonian graph is a bicubic (i.e., bipartite cubic graph) that is nonhamiltonian (i.e., that does not possess a Hamiltonian cycle). Tutte (1971) conjectured ...

The Knödel graph W_(Delta,n) is a regular bipartite graph of vertex degree Delta on n nodes for even n>=2 and 1<=Delta<=|_log_2n_| with edges defined as follows. Label the ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...