WCSE

The β-differential for the Square Lattice

Abstract— In this paper, we study the β-differentials of the square lattice graphs. By the adjacent vertex number sequence of a given vertex set, some closed-form formulas of the β-differentials in the square lattice graphs are obtained. The results show that the differentials of the square lattice graphs are periodic, so we can get the differential recurrence formula of the general square lattice graph.

Index Terms— differential of a graph, domination number, the square lattice

Qiannan Niu
School of Mathematics and Statistics, Qinghai Normal University, CHINA
Haizhen Ren
School of Mathematics and Statistics, Qinghai Normal University, CHINA
Academy of Plateau Science and Sustainability, CHINA
Lei Zhang
School of Mathematics and Statistics, Qinghai Normal University, CHINA

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Cite: Qiannan Niu, Haizhen Ren, Lei Zhang, "The β-differential for the Square Lattice," 2021 The 11th International Workshop on Computer Science and Engineering (WCSE 2021), pp. 155-162, Shanghai, China, June 19-21, 2021.