论文信息 - Tree counting polynomials for labelled graphs part I: Properties

Tree counting polynomials for labelled graphs part I: Properties

Abstract The properties of special pairs of tree counting polynomials that relate to a class of incomplete graphs and their complements are presented. These polynomial pairs are related by the previously defined binary complementing operation.In contrast with alternative graph representations, they offer the possibility of serving as a convenient signature for the specific configurations. In Part II, a new constructive procedure is presented for deriving these polynomials. It is shown that the new algorithmic approach facilities obtaining the polynomials for cases not readily obtained by use of generic factors of the basic subgraphs.

S. D. Bedrosian

[1] Earl Glen Whitehead. Stirling Number Identities from Chromatic Polynomials , 1978, J. Comb. Theory, Ser. A.

[2] A. Mowshowitz. The characteristic polynomial of a graph , 1972 .

[3] Coefficient relationship between rook and chromatic polynomials , 1976 .

[4] S. Bedrosian. Formulas for the Number of Trees in a Network , 1961 .

[5] Alexander K. Kelmans. Comparison of graphs by their number of spanning trees , 1976, Discret. Math..

[6] F. Harary. The Determinant of the Adjacency Matrix of a Graph , 1962 .

[7] E. J. Farrell,et al. On a general class of graph polynomials , 1979, J. Comb. Theory, Ser. B.

[8] Properties and Applications of a Class of Polynomials , 1973 .

[9] Richard James Duffin,et al. An analysis of the Wang algebra of networks , 1959 .

[10] Robert R. Korfhage,et al. Sigma-polynomials and Graph Coloring , 1978, Journal of combinatorial theory. Series B (Print).

[11] Alexander K. Kelmans,et al. Nonisomorphic Trees with the Same T-Polynomial , 1977, Inf. Process. Lett..

[12] S. D. Bedrosian. Generating formulas for the number of trees in a graph , 1964 .

[13] A. Kelmans,et al. A certain polynomial of a graph and graphs with an extremal number of trees , 1974 .

[14] J. Moon. Counting labelled trees , 1970 .