Amorphic Cellular Rings

The enumeration problem for cellular subrings of a given cellular ring has found numerous applications in combinatorics and graph theory (see for example [17], [22]). Usually one uses a computer to solve this problem. A general idea underlying searching algorithms for the enumeration of subrings was proposed in [19] and consists of the following.

[1]  M. Marcus,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[2]  A. A. Li︠a︡punov.  Problems in Cybernetics , 1961, Nature.

[3]  H. Wielandt,et al.  Finite Permutation Groups , 1964 .

[4]  N. Biggs.  Algebraic Graph Theory: COLOURING PROBLEMS , 1974 .

[5]  S. S. Shrikhande,et al.  Nonisomorphic Solutions of pseudo‐(3.5,2) and pseudo‐(3,6,3) graphs , 1970 .

[6]  B. Weisfeiler.  On construction and identification of graphs , 1976 .

[7]  S. Shrikhande.  The uniqueness of the L_2 association scheme , 1958 .

[8]  J. J. Seidel,et al.  SYMMETRIC HADAMARD MATRICES OF ORDER 36 , 1970 .

[9]  Dale M. Mesner,et al.  A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties , 1967 .

[10]  J. H. Lint,et al.  Graph theory, coding theory, and block designs , 1975 .

[11]  R. Bellman,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[12]  S. S. Shrikhande,et al.  The Uniqueness of the $\mathrm{L}_2$ Association Scheme , 1959 .

[13]  Reinhard Pöschel,et al.  Funktionen- und Relationenalgebren , 1979 .

[14]  R. H. Bruck.  Finite nets. II. Uniqueness and imbedding. , 1963 .

[15]  Russell W. Myers,et al.  1-homogeneous Graphs , 1985, Discret. Math..

[16]  Xavier L. Hubaut,et al.  Strongly regular graphs , 1975, Discret. Math..

[17]  Frank Harary,et al.  Graph Theory , 2016 .

[18]  R. C. Bose.  Strongly regular graphs, partial geometries and partially balanced designs. , 1963 .