Graphs which their certain polynomials have few distinct roots- a survey

2011/12/05 by ‎Saeid Alikhani, Saeid Alikhani, Alikhani, Saeid
Computer Science · Mathematics · #05C69 #11B83 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO #msc:05C69 #msc:11B83

paper · pdf · doi:10.48550/arxiv.1112.0838

21 pages (with figures)

arxiv created 2011/12/05 · openalex publication_date 2011/12/05 · arxiv updated 2011/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G = (V;E) be a simple graph. We consider domination polynomial, matching polynomial and edge cover polynomial of G. Graphs which their polynomials have few roots can give sometimes a very surprising information about the structure of the graph. In this paper we study graphs which their domination polynomial, independence polynomial and edge cover polynomial have few roots.

Related

• Graphs with few matching roots
• Some families of graphs with no nonzero real domination roots
• Some new results on domination roots of a graph
• On the independent domination polynomial of a graph
• An atlas of domination polynomials of graphs of order at most six