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The circular graph C(n, m) is such a graph that whose vertex set is {v 0 , v 1 , v 2 , · · · , v n−1 } and edge set is {v i v i+1 , v i v i+m | i = 0, 1, · · · , n − 1}, where m, n are natural numbers, addition is modulo n, and 2 ≤ m ≤ n 2. This paper shows the crossing number of the circular graph C(2m + 2, m)(m ≥ 3) is m + 1.

- Jinhua Wang, Dengju Ma
- Graphs and Combinatorics
- 2010

- Dengju Ma, Hengfeng Zhu, Jianbao He
- J. Comb. Optim.
- 2014

- Dengju Ma
- Australasian J. Combinatorics
- 2017

Let Pm Pn be the strong product of two paths Pm and Pn. In 2013, Klešč et al. conjectured that the crossing number of Pm Pn is equal to (m − 1)(n − 1) − 4 for m ≥ 4 and n ≥ 4. In this paper we show that the above conjecture is true except when m = 4 and n = 4, and that the crossing number of P4 P4 is four.

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds. Also, we give a formula for calculating the length of minimum cycle base of… (More)

- Dengju Ma
- Discrete Applied Mathematics
- 2014

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