2021/12/09 by A. V. Jayanthan, Jayanthan, A. V., Rajib Sarkar +1
Computer Science · Mathematics · #05E40 #13C13 #13D02 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph Labeling and Dimension Problems #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2112.04835
openalex publication_date 2021/12/09 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
Let G be a simple connected non-complete graph and JG be its binomial edge ideal in a polynomial ring S. Using certain invariants associated to graphs, say U(G), Banerjee and Núñez-Betancourt gave an upper bound for the depth of S/JG, and Rouzbahani Malayeri, Saeedi Madani and Kiani obtained a lower bound, say L(G). Hibi and Saeedi Madani gave a structural classification of graphs satisfying L(G)=U(G). In this article, we give structural classification of graphs satisfying L(G)+1=U(G). We also compute the depth of S/JG for all such graphs G.