Independence Polynomials of graphs and degree of $h$-polynomials of edge ideals
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917344097337344 |
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| author | Tan, Ton That Quoc |
| author_facet | Tan, Ton That Quoc |
| contents | Let $G=(V,E)$ be a finite simple graph. In this paper, we study the degree of the $h$-polynomial of the edge ideal of $G$ in relation to the independence number of $G$. Our approach is based on the value of the independence polynomial of $G$ at $-1$ and its derivatives at $-1$. We establish a necessary and sufficient condition for the equality $° h_{R/I(G)}(t)=α(G)$. As consequences, we obtain combinatorial formulas for the degree of the $h$-polynomial for several classes of graphs, including paths, cycles, bipartite graphs, Cameron--Walker graphs, and antiregular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Independence Polynomials of graphs and degree of $h$-polynomials of edge ideals Tan, Ton That Quoc Commutative Algebra Combinatorics 13D02, 13D40, 13C70, 05C31 Let $G=(V,E)$ be a finite simple graph. In this paper, we study the degree of the $h$-polynomial of the edge ideal of $G$ in relation to the independence number of $G$. Our approach is based on the value of the independence polynomial of $G$ at $-1$ and its derivatives at $-1$. We establish a necessary and sufficient condition for the equality $° h_{R/I(G)}(t)=α(G)$. As consequences, we obtain combinatorial formulas for the degree of the $h$-polynomial for several classes of graphs, including paths, cycles, bipartite graphs, Cameron--Walker graphs, and antiregular graphs. |
| title | Independence Polynomials of graphs and degree of $h$-polynomials of edge ideals |
| topic | Commutative Algebra Combinatorics 13D02, 13D40, 13C70, 05C31 |
| url | https://arxiv.org/abs/2602.12169 |