Overlap matrices and total imbedding distributions

Abstract The concept of genus distribution of graphs is generalized to include nonorientable imbeddings. Explicit computations of the total imbedding distributions for several interesting graph classes are given. These computations are an illustration of the power of a theorem by Mohar that relates topological types of imbedding surfaces to ranks of the corresponding overlap matrices.

[1]  Jianer Chen,et al.  Limit points for average genus II. 2-Connected non-simplicial graphs , 1992, J. Comb. Theory, Ser. B.

[2]  Jonathan L. Gross,et al.  Genus distributions for bouquets of circles , 1989, J. Comb. Theory, Ser. B.

[3]  S. Gill Williamson,et al.  A Comprehensive Introduction to Linear Algebra , 1989 .

[4]  Nguyen Huy Xuong,et al.  How to determine the maximum genus of a graph , 1979, J. Comb. Theory, Ser. B.

[5]  Jianer Chen,et al.  Limit points for average genus. I. 3-Connected and 2-connected simplicial graphs , 1992, J. Comb. Theory, Ser. B.

[6]  Jianer Chen,et al.  Kuratowski-Type Theorems for Average Genus , 1993, J. Comb. Theory, Ser. B.

[7]  Jack Edmonds,et al.  On the surface duality of linear graphs , 1965 .

[8]  Jonathan L. Gross,et al.  Hierarchy for imbedding-distribution invariants of a graph , 1987, J. Graph Theory.

[9]  Jonathan L. Gross,et al.  On the average genus of a graph , 1993, Graphs Comb..

[10]  A. White.  Graphs, Groups and Surfaces , 1973 .

[11]  Bojan Mohar,et al.  An obstruction to embedding graphs in surfaces , 1989, Discret. Math..

[12]  Jianer Chen.  The distribution of graph imbeddings on topological surfaces , 1991 .

[13]  Lyle Andrew Mcgeoch,et al.  Algorithms for two graph problems: computing maximum-genus imbeddings and the two-server problem , 1987 .

[14]  Richard Statman,et al.  Genus distributions for two classes of graphs , 1989, J. Comb. Theory, Ser. B.

[15]  Robert G. Rieper.  The Enumeration of Graph Imbeddings , 1990 .