Perfect 4-Colorings of the 3-Regular Graphs of Order at Most 8

被引:0
作者
Vahedi, Z. [1 ]
Alaeiyan, M. [2 ]
Maghasedi, M. [1 ]
机构
[1] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran
[2] Iran Univ Sci & Technol, Sch Math, Math, Tehran 16846, Iran
关键词
Perfect coloring; Parameter matrices; Cubic graph; Equitable partition; 2-COLORINGS;
D O I
10.30495/JME.2022.1501
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The perfect m-coloring with matrix A = [a(ij)](i,j is an element of) {1, ...,m} of a graph G = (V, E) with {1, ...., m} color is a vertex coloring of G with m-color so that the number of vertices in color j adjacent to a fixed vertex in color i is a(ij), independent of the choice of vertex in color i. The matrix A = [a(ij)](i,j is an element of{1, ...,m} )is called the parameter matrix. We study the perfect 4-colorings of the 3-regular graphs of order at most 8, that is, we determine a list of all color parameter matrices corresponding to perfect 4-colorings of 3-regular graphs of orders 4, 6, and 8.
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页数:16
相关论文
共 8 条
[1]  
Alaeiyan M, 2017, ELECTRON J GRAPH THE, V5, P194, DOI 10.5614/ejgta.2017.5.2.3
[2]  
Avgustinovich S.V., 2011, J. Appl. Ind. Math., V5, P19
[3]  
Avgustinovich S, 2008, LECT NOTES COMPUT SC, V5228, P11, DOI 10.1007/978-3-540-87448-5_2
[4]   Perfect 2-colorings of a hypercube [J].
Fon-Der-Flaass, D. G. .
SIBERIAN MATHEMATICAL JOURNAL, 2007, 48 (04) :740-745
[5]  
Fon-Der-Flaass DG, 2007, SIB ELECTRON MATH RE, V4, P292
[6]  
Fon-Der-Flaass DG, 2007, SIB ELECTRON MATH RE, V4, P133
[7]   On perfect 2-colorings of Johnson graphs J(v, 3) [J].
Gavrilyuk, Alexander L. ;
Goryainov, Sergey V. .
Journal of Combinatorial Designs, 2013, 21 (06) :232-252
[8]   Compact graphs and equitable partitions [J].
Godsil, CD .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 255 :259-266