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Semi-cartesian product of graphs

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Abstract

In this paper, we define a kind of new product graphs with hexagonal inner faces, called semi-cartesian products, so that they directly link with hexagonal system, e.g., the semi-cartesian product of an even cycle and a path is a zigzag polyhex nanotube, a path and an even cycle is an armchair polyhex nanotube, two even cycles is a polyhex nanotorus and two paths is a polyhex lattice. Then we consider the distance in a semi-cartesian product and show two formulas to calculate the distance of two vertices and the sum of all pair of distances. Moreover we illustrate that the applying of the semi-cartesian products would be greatly simplifies the calculation of the distances in the carbon nanotubes and polyhex nanotorus by presenting some examples.

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Acknowledgments

This work was supported by the National Science Foundation of China No. 11141001.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen , 361005, People’s Republic of China

    Metrose Metsidik

  2. College of Mathematical Sciences, Xinjiang Normal University, Ürümqi , 830054, People’s Republic of China

    Metrose Metsidik

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  1. Metrose Metsidik
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Correspondence to Metrose Metsidik.

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Metsidik, M. Semi-cartesian product of graphs. J Math Chem 52, 856–865 (2014). https://doi.org/10.1007/s10910-013-0297-6

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  • DOI: https://doi.org/10.1007/s10910-013-0297-6

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