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https://www.um.edu.mt/library/oar/handle/123456789/109166| Title: | On the adjacency matrix and the colouring of graphs |
| Authors: | Sciriha, Irene Marino, Corinna M. |
| Keywords: | Graph theory -- Data processing Matrices -- Mathematical models Graph coloring Eulerian graph theory Hamiltonian graph theory |
| Issue Date: | 2001 |
| Publisher: | Utilitas Mathematica Pub |
| Citation: | Sciriha, I., & Marino, M. C. (2001). On the adjacency matrix and the colouring of graphs. Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, Louisiana. Congressus Numerantium, 148, 43-63. |
| Abstract: | A planar graph, G, can be drawn on a plane in such a way that no two edges intersect. It is said to be maximal planar if no edge can be added without losing planarity. Each vertex of an Eulerian graph is of even degree. We show that the chromatic number of a maximal planar graph is 3 if and only if it is Eulerian. From the adjacency matrix of a planar graph, the monochromatic classes can be deduced and unique colourability determined. Moreover, we show that certain transformations on a graph G determine the chromatic number x(G). |
| URI: | https://www.um.edu.mt/library/oar/handle/123456789/109166 |
| Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| On the adjacency matrix and the colouring of graphs 2001.pdf Restricted Access | 842.87 kB | Adobe PDF | View/Open Request a copy |
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