Damghan UniversityGlobal Analysis and Discrete Mathematics2476-53416120210801Perfect 4-Colorings of the 3-Regular Graphs of Order 1013114221010.22128/gadm.2021.439.1048ENZeinabVahediDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranMohammadMaghasediDepartment of Mathematics, Karaj Branch, Islamic Azad
University, Karaj, Iran0000-0001-6551-6620MehdiAlaeiyanIran University of Science and Technology0000-0003-2185-5967Journal Article20210726The perfect <em>m</em>-coloring with matrix <em>A</em> = <em>[a<sub>ij</sub> ]<sub>i,j∈{1,...,m}</sub></em> of a graph <em>G = (V, E)</em> with {<em>1, . . . , m</em>} color is a vertices coloring of G with <em>m</em>-color so that number of vertex in color j adjacent to a fixed vertex in color i is a<sub>ij</sub> , independent of the choice of vertex in color i. The matrix A = [a<sub>ij</sub> ]<sub>i,j∈{1,...,m} </sub>is called the parameter matrix.<br />We study the perfect 4-colorings of the 3-regular graphs of order 10, that is, we determine a list of all color parameter matrices corresponding to perfect colorings of 3-regular graphs of order 10. https://gadm.du.ac.ir/article_210_611fc6cb4f723872135a7b02c25d70ee.pdf