Graph Polynomials

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.

Matthias Dehmer studied mathematics at the University of Siegen (Germany) and received his Ph.D. in computer science from the Technical University of Darmstadt (Germany). Afterwards, he was a research fellow at Vienna Bio Center (Austria), Vienna University of Technology, and University of Coimbra (Portugal). He obtained his habilitation in applied discrete mathematics from the Vienna University of Technology. Currently, he is Professor at UMIT - The Health and Life Sciences University (Austria) and also has a position at Bundeswehr Universit¨at M¨unchen (Germany). His research interests are in graph theory, complex networks, complexity, machine learning and information theory. In particular, he is also working on machine learning-based methods to design new data analysis methods for solving problems in computational biology. He has more than 170 publications in applied mathematics, computer science and related disciplines. Yongtang Shi studied mathematics at Northwest University (Xi’an, China) and received his Ph.D in applied mathematics from Nankai University (Tianjin, China). Currently, he is an associate professor at the Center for Combinatorics of Nankai University. He visited some institutes and universities at Germany, Austria and Canada. His research interests are in graph theory and its applications, especially the applications of graph theory in mathematical chemistry, computer science and information theory. He has about 50 publications in graph theory and its applications. Ivan Gutman obtained his PhD degree in chemistry at the Faculty of Science, University of Zagreb, and also a PhD degree in mathematics, at the Faculty of Electrical Engineering, University of Belgrade. He is a member of the Serbian Academy of Sciences and Arts 1998; a member of the International Academy