2020/09/01 by Reza Jafarpour-Golzari, Jafarpour-Golzari, Reza
Computer Science · Mathematics · #05C07 (Primary) 05C31 #05C76 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2009.00488
openalex publication_date 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for realizability of a sequence of polynomials with coefficients in positive integers. Also we calculate the degree polynomial for vertises of join, Cartesian product, tensor product, and lexicographic product of two simple graphs and for vertices of the complement of a simple graph. Some examples, counterexamples, and open problems concerning to this subjects, is given as well