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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 ...

If the Tutte polynomial T(x,y) of a graph G is given by sumt_(rs)x^ry^s, then the matrix (t_(rs)) is called the rank matrix of G. For example, the Tutte matrix of the ...

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

The set E of edges of a loopless graph (V,E), being a set of unordered pairs of elements of V, constitutes an adjacency relation on V. Formally, an adjacency relation is any ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

The (upper) matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...