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Mathematics > Combinatorics

arXiv:2212.04253 (math)
[Submitted on 8 Dec 2022]

Title:Triangle-free projective-planar graphs with diameter two: domination and characterization

Authors:Dibyayan Chakraborty, Sandip Das, Srijit Mukherjee, Uma kant Sahoo, Sagnik Sen
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Abstract:In 1975, Plesník 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.
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
Cite as: arXiv:2212.04253 [math.CO]
  (or arXiv:2212.04253v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2212.04253

Submission history

From: Dibyayan Chakraborty [view email]
[v1] Thu, 8 Dec 2022 13:10:15 UTC (337 KB)
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