Characterization of general position sets and its applications to cographs and bipartite graphs

Anand, Bijo S.; V., Ullas Chandran S.; Changat, Manoj; Klavžar, Sandi; Thomas, Elias John

doi:10.48550/arxiv.1812.08460

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2019

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“…If G = (V (G), E(G)) is a graph, then S ⊆ V (G) is a general position set if no triple of vertices from S lie on a common geodesic in G. The general position problem is to find a largest general position set of G, the order of such a set is the general position number gp(G) of G. A general position set of G of order gp(G) is shortly called gp-set. The general position problem has been further studied in a sequence of very recent papers [1,2,8,10].…”

Section: Introductionmentioning

confidence: 99%

The general position problem and strong resolving graphs

Klavžar

Yero

2019

Open Mathematics

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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. It is proved that gp(G) ≥ ω(G SR , where G SR is the strong resolving graph of G, and ω(G SR ) is its clique number. That the bound is sharp is demonstrated with numerous constructions including for instance direct products of complete graphs and different families of strong products, of generalized lexicographic products, and of rooted product graphs.

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Section: Introductionmentioning

confidence: 99%