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An (n,k)-firecracker is a graph obtained by the concatenation of n k-stars by linking one leaf from each (Chen et al. 1997, Gallian 2007). Firecracker graphs are graceful ...

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 ...

A quasi-cubic 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 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

A topological space X is semilocally simply connected (also called semilocally 1-connected) if every point x in X has a neighborhood U such that any loop L:[0,1]->U with ...

A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

The Biggs-Smith graph is cubic symmetric graph F_(102)A on 102 vertices and 153 edges that is also distance-regular with intersection array {3,2,2,2,1,1,1;1,1,1,1,1,1,3} and ...

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