The Crossing Number of Circulant Graph C(3k+1;{1,k}) on the Projective Plane

TL;DR

This paper determines the crossing number of a specific class of circulant graphs on the projective plane, establishing it as equal to parameter k for all k ≥ 3.

Contribution

It provides a precise crossing number calculation for circulant graphs C(3k+1;{1,k}) on the projective plane, a previously unresolved problem.

Findings

Crossing number of C(3k+1;{1,k}) on the projective plane is k for k ≥ 3.

Established exact crossing number for this class of circulant graphs.

Contributed to topological graph theory by solving a specific crossing number problem.

Abstract

In this paper, we prove that the crossing number of circulant graph $C(3k+1;\{1,k\})$ on the projective plane is $k$ for $k \geq 3$.