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The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

The skewness of a graph G is the minimum number of edges whose removal results in a planar graph (Harary 1994, p. 124). The skewness is sometimes denoted mu(G) (Cimikowski ...

Graph smoothing, also known as smoothing away or smoothing out, is the process of replacing edges e^'=v_iv_j and e^('')=v_jv_k incident at a vertex v_j of vertex degree 2 by ...

The square of a graph is defined as its second graph power. The square of any biconnected graph is Hamiltonian (Fleischner 1974, Skiena 1990, p. 231). Mukhopadhyay (1967) has ...

An edge subdivision is the insertion of a new vertex v_j in the middle of an exiting edge e=v_iv_k accompanied by the joining of the original edge endpoints with the new ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

A graphoid consists of a set M of elements together with two collections C and D of nonempty subsets of M, called circuits and cocircuits respectively, such that 1. For any C ...

An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of ...

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 ...

The polyhedron compound of the great icosahedron (U_(53)) and the small stellated dodecahedron (U_(34)), sometimes known as the great cid. Four faces meet at each edge of the ...