This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
The Alliance Polynomial of a Graph. Aspects of the Interlace Polynomial of a Graph. The clique-transversal set problem in clawfree graphs with degree at most 4. Permanental Polynomials of Graphs. Tutte polynomial and its generalizations. Graphs characterized by various polynomials. Recurrence relations of graph polynomials. Independence polynomials of k-tree related graphs. Generatingfunctionology for Graph Polynomials. Symmetric representations and the connection with linear recurrences. From the Ising and Potts model to the general graph homomorphism polynomial.