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An ungraceful graph is a simple graph that does not possess a graceful labeling, i.e., a graph that is not a graceful graph (Gardner 1972). Such graphs have also been termed ...

A stacked (or generalized) prism graph Y_(m,n) is a simple graph given by the graph Cartesian product Y_(m,n)=C_m square P_n (Gallian 2007) for positive integers m,n with ...

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

The n-double cone graph is the name given in the work to the graphs that geometrically correspond to a double cone obtained by connecting all vertices of two C_n cycle graphs ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

The nth-order Menger sponge graph is the connectivity graph of cubes in the nth iteration of the Menger sponge fractal. The first two iterations are shown above. The n-Menger ...