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A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The Harary index of a graph G on n vertices was defined by Plavšić et al. (1993) as H(G)=1/2sum_(i=1)^nsum_(j=1)^n(RD)_(ij), (1) where (RD)_(ij)={D_(ij)^(-1) if i!=j; 0 if ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The folded n-cube graph, perhaps better termed "folded hypercube graph," is a graph obtained by merging vertices of the n-hypercube graph Q_n that are antipodal, i.e., lie at ...

Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is not ...

A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...