Original scientific paper

https://doi.org/10.5562/cca3008

Euler Characteristic of Polyhedral Graphs

Atena Pîrvan-Moldovan ; Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028 Cluj, Romania
Mircea V. Diudea ; Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028 Cluj, Romania

Abstract

Euler characteristic is a topological invariant, a number that describes the shape or structure of a topological space, irrespective of the way it is bent. Many operations on topological spaces may be expressed by means of Euler characteristic. Counting polyhedral graph figures is directly related to Euler characteristic. This paper illustrates the Euler characteristic involvement in figure counting of polyhedral graphs designed by operations on maps. This number is also calculated in truncated cubic network and hypercube. Spongy hypercubes are built up by embedding the hypercube in polyhedral graphs, of which figures are calculated combinatorially by a formula that accounts for their spongy character. Euler formula can be useful in chemistry and crystallography to check the consistency of an assumed structure.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Keywords

Euler characteristic; polyhedral graph; hypercube; map operation

Hrčak ID:

180000

URI

https://hrcak.srce.hr/180000

Publication date:

19.12.2016.

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