Article
Version 1
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Where Are Planar 0-Vertex Graphs Hiding?
Version 1
: Received: 19 August 2024 / Approved: 19 August 2024 / Online: 19 August 2024 (14:02:09 CEST)
How to cite: turulski, J. Where Are Planar 0-Vertex Graphs Hiding?. Preprints 2024, 2024081357. https://doi.org/10.20944/preprints202408.1357.v1 turulski, J. Where Are Planar 0-Vertex Graphs Hiding?. Preprints 2024, 2024081357. https://doi.org/10.20944/preprints202408.1357.v1
Abstract
Euler's theorem about the relationship between the numbers of individual elements of planar graphs (vertices, edges, faces) is also satisfied when the graph has zero vertices. The problem of the existence or not of such graphs has so far been the subject of very few studies. Plus, research that didn't prove anything. The paper presents an interpretation of this kind of graphs as mathematical formations lying on piecewise smooth surfaces. The lines of intersection of two or more smooth surfaces (faces of a graph) form edges without a vertex of the graph. The elementary properties of such graphs are discussed, the method of counting non-isomorphic 0-vertex graphs and their importance in physics and chemistry are given.
Keywords
chemical graph; planar graph; Euler's formula; invariant states
Subject
Chemistry and Materials Science, Theoretical Chemistry
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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