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A graph is k-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given ...

Let G be a simple graph with nonsingular (0,1) adjacency matrix A. If all the diagonal entries of the matrix inverse A^(-1) are zero and all the off-diagonal entries of ...

A quasi-qunitic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...

The truncated great dodecahedral graph is the skeleton of the small stellated truncated dodecahedron and truncated great dodecahedron. It is illustrated above in a number of ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

The small snub icosicosidodecahedral graph is the skeleton of the small retrosnub icosicosidodecahedron and small snub icosicosidodecahedron. It is illustrated above in a ...