Graphs with 1-Hamiltonian-connected cubes |
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Authors: | Linda Lesniak |
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Institution: | Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49001 USA |
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Abstract: | The cube G3 of a connected graph G is that graph having the same vertex set as G and in which two distinct vertices are adjacent if and only if their distance in G is at most three. A Hamiltonian-connected graph has the property that every two distinct vertices are joined by a Hamiltonian path. A graph G is 1-Hamiltonian-connected if, for every vertex w of G, the graphs G and G?w are Hamiltonian-connected. A characterization of graphs whose cubes are 1-Hamiltonian-connected is presented. |
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