Genus of the cartesian product of triangles
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Electronic Journal of Combinatorics |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | graph; cartesian product; genus; embedding; triangle; symmetric embedding; Cayley graph; Cayley map; genus range; group |
| Description | We investigate the orientable genus of G(n), the cartesian product of n triangles, with a particular attention paid to the two smallest unsolved cases n = 4 and 5. Using a lifting method we present a general construction of a low -genus embedding of G(n) using a low-genus embedding of G(n-1). Combining this method with a computer search and a careful analysis of face structure we show that 30 <= gamma (G(4)) <= 37 and 133 <= gamma(G(5)) <= 190. Moreover, our computer search resulted in more than 1300 non isomorphic minimum -genus embeddings of G(3). We also introduce genus range of a group and (strong) symmetric genus range of a Cayley graph and of a group. The (strong) symmetric genus range of irredundant Cayley graphs of Z(p)(n) is calculated for all odd primes p. |
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