The general position number of integer lattices
| Autor: | Gregor Rus, Sandi Klavžar |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Geodesic Applied Mathematics 020206 networking & telecommunications 02 engineering and technology Cartesian product Combinatorics Computational Mathematics symbols.namesake 020901 industrial engineering & automation Cardinality Integer Path (graph theory) 0202 electrical engineering electronic engineering information engineering symbols Lattice graph General position Connectivity Mathematics |
| Zdroj: | Applied Mathematics and Computation. 390:125664 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2020.125664 |
| Popis: | The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic. The n-dimensional grid graph P ∞ n is the Cartesian product of n copies of the two-way infinite path P∞. It is proved that if n ∈ N , then gp ( P ∞ n ) = 2 2 n − 1 . The result was earlier known only for n ∈ {1, 2} and partially for n = 3 . |
| Databáze: | OpenAIRE |
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