# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

J. Wang, J.L. Cai, S.X. Lv, Y.Q. Huang

Title:

The crossing number of hexagonal graph $H_{3,n}$ in the projective plane

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-03-12, Revised: 2019-08-18, Accepted: 2019-09-10, https://doi.org/10.7151/dmgt.2251

Abstract:

Thomassen described all (except finitely many) regular tilings of the torus $S_1$ and the Klein bottle $N_2$ into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many researchers made great efforts to investigate the crossing number of the Cartesian product of an $m$-cycle and an $n$-cycle, which is a special kind of (4,4)-tilings, either in the plane or in the projective plane. In this paper we study the crossing number of the hexagonal graph $H_{3,n}$ $(n\ge 2)$, which is a special kind of (3,6)-tilings, in the projective plane, and prove that \vspace{-1mm} $cr_{N_1}(H_{3,n})= \left\{ \begin{array}{ll} 0, \quad & n=2, <br> n-1, \quad & n\ge 3. \end{array}\right.$

Keywords:

projective plane, crossing number, hexagonal graph, drawing