Derivatives and real roots of graph polynomials

2016/01/08 by Xueliang Li, Yongtang Shi, Li, Xueliang +1
Mathematics · #05C31 #05C35 #05C50 #05C90 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C31 #msc:05C35 #msc:05C50 #msc:05C90

paper · pdf · doi:10.48550/arxiv.1601.01843

14 pages. This will appear as a chapter in a book: Graph Polynomials, Edited by M. Dehmer et al., CRC Press/Taylor & Francis Group, LLC

arxiv created 2016/01/12 · arxiv updated 2016/01/13

Abstract

Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the derivative and real roots of graph polynomials, which have applications in chemistry, control theory and computer science. Related to the derivatives of graph polynomials, polynomial reconstruction of the matching polynomial is also introduced.

Related

• On the location of roots of graph polynomials
• Graph polynomials: some questions on the edge
• Graph polynomials and their applications II: Interrelations and interpretations
• Degree polynomial of vertices in a graph and its behavior under graph operations
• Polynomial reconstruction of the matching polynomial