M. Alaeiyan - Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran. A. Abedi - Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran.
A perfect \(2\)-coloring of a graph \(G\) with a matrix \(A=\{a_{ij}\}_{i,j=1,2}\) is a coloring of the vertices of \(G\) into the set of colors \(\{1,2\}\) such that the number of vertices of the color \(j\) adjacent with the fixed vertex \(x\) of the color \(i\) does not depend on a choice of the vertex \(x\) and equals to \(a_{ij}\). The matrix \(A\) is called the parameter matrix of a perfect coloring. We can consider perfect coloring as a generalization of the concept of completely regular codes presented by P. Delsarte for the first time. The parameter matrices of all perfect \(2\)-colorings of the Johnson graph \(J(10,\,3)\) are listed in this paper.
M. Alaeiyan, A. Abedi, Perfect \(2\)-Colorings of Johnson Graph \(J(10,\,3)\), Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6344--6348
Alaeiyan M., Abedi A., Perfect \(2\)-Colorings of Johnson Graph \(J(10,\,3)\). J. Nonlinear Sci. Appl. (2017); 10(12):6344--6348
Alaeiyan, M., Abedi, A.. "Perfect \(2\)-Colorings of Johnson Graph \(J(10,\,3)\)." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6344--6348
