Triangle-free projective-planar graphs with diameter two: domination and characterization
In 1975, Plesn\'ik characterized all triangle-free planar graphs as having a diameter $2$. We characterize all triangle-free projective-planar graphs having a diameter $2$ and discuss some applications. In particular, the main result is applied to calculate the analogue of clique numbers for gr...
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| Zusammenfassung: | In 1975, Plesn\'ik characterized all triangle-free planar graphs as having a
diameter $2$. We characterize all triangle-free projective-planar graphs having
a diameter $2$ and discuss some applications. In particular, the main result is
applied to calculate the analogue of clique numbers for graphs, namely, colored
mixed graphs, having different types of arcs and edges. |
|---|---|
| DOI: | 10.48550/arxiv.2212.04253 |