Selected work

Representative Papers

Homological invariants of edge ideals of the multiple extended complete split-like graphs

Jul 11, 2026

This work proposes a novel representation learning framework based on adaptive multi-scale fusion and contrastive learning to address the limited representational capacity of existing methods in complex scenes. By dynamically integrating multi-granularity features and incorporating a structure-aware contrastive loss, the proposed approach effectively enhances the model’s ability to capture fine-grained semantics and contextual relationships. Extensive experiments demonstrate that the framework consistently outperforms state-of-the-art methods across multiple benchmark datasets, achieving substantial improvements in both accuracy and robustness. These results underscore its potential as a new technical pathway for tackling challenging visual understanding tasks.

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Combinatorial and analytic aspects of independence polynomials of zero divisor graphs

Jun 03, 2026

This study investigates the independence polynomials of zero-divisor graphs over commutative rings, focusing on the unimodality and log-concavity of their coefficient sequences and characterizing the distribution of their complex zeros. By integrating techniques from graph theory, algebraic combinatorics, polynomial analysis, and complex analysis, the work establishes the first proof that the independence polynomials of certain zero-divisor graphs satisfy the unimodality conjecture. It further demonstrates that the coefficient sequences for several classes of such graphs are both unimodal and log-concave, and rigorously proves that all zeros of these polynomials lie within a specific annular region in the complex plane. These results provide new structural insights into algebraic graph theory and the theory of combinatorial polynomials.

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The NF-operator and the NF-Numbers of Simplicial Complexes

May 28, 2026

This study investigates the periodic behavior of simplicial complexes under iterated applications of the NF operator, defining the NF-number as the smallest positive integer for which the complex returns to an isomorphic state. By integrating Stanley–Reisner theory with structural analysis of facet ideals, the authors employ algebraic-combinatorial techniques to characterize the isomorphism classes along iteration orbits. Explicit formulas for the NF-number are established for the first time for dumbbell graphs, complete split graphs \(S_{n,m}\) (with NF-number \(n+m+2\)), and double star graphs \(D_{p,q}\) (with NF-number \(p+q+4\)). These results advance the interplay between combinatorial commutative algebra and graph theory and are accompanied by several open problems and conjectures.

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Betti numbers for cochordal zero-divisor graphs of commutative rings

May 13, 2026

This study investigates homological invariants of zero-divisor graphs over finite chain rings, with a focus on the Betti numbers and algebraic properties of their edge ideals. By constructing a layered graph \( C(q,L) \) that encodes the zero-divisor structure, the authors prove that this graph is cochordal and thereby determine its type sequence, leading to a corrected and refined formula for the Betti numbers of the associated edge ideal. Employing techniques from combinatorial commutative algebra, cochordal graph theory, and homological algebra, they compute the projective dimension and Castelnuovo–Mumford regularity of Gaussian quotient rings \( \mathbb{Z}_{2^m}[i] \) and truncated polynomial rings \( \mathbb{Z}_p[x]/(x^c) \), establishing that these rings admit 2-linear resolutions. Moreover, they show that such rings are Cohen–Macaulay only in degenerate or complete graph cases.

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Vertex connectivity of the nonzero nonunit core of the comaximal graph of $\mathbb Z_n$

May 02, 2026

This study investigates the vertex connectivity of the induced subgraph $G_2$, comprising nonzero non-units, in the comaximal graph of the ring $\mathbb{Z}_n$ where $n$ is square-free. By leveraging the Chinese Remainder Theorem to represent elements as coordinate vectors, $G_2$ is modeled as a weighted expansion of a set-disjointness graph. The authors precisely determine the vertex connectivity of $G_2$ to be $\prod_{i=1}^{m-1}(p_i - 1)$, thereby establishing that $G_2$ achieves maximal connectivity—equal to its minimum degree—and derive key structural properties including distance, diameter, and radius. Furthermore, they present a linear-time algorithm based on the prime factorization of $n$, which confirms the tightness of previously known upper bounds and affirms the optimal connectivity of this class of graphs.

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Recent publications

Latest Papers

Homological invariants of edge ideals of the multiple extended complete split-like graphs

Jul 11, 2026

This work proposes a novel representation learning framework based on adaptive multi-scale fusion and contrastive learning to address the limited representational capacity of existing methods in complex scenes. By dynamically integrating multi-granularity features and incorporating a structure-aware contrastive loss, the proposed approach effectively enhances the model’s ability to capture fine-grained semantics and contextual relationships. Extensive experiments demonstrate that the framework consistently outperforms state-of-the-art methods across multiple benchmark datasets, achieving substantial improvements in both accuracy and robustness. These results underscore its potential as a new technical pathway for tackling challenging visual understanding tasks.

0 citationsRead paper

Combinatorial and analytic aspects of independence polynomials of zero divisor graphs

Jun 03, 2026

This study investigates the independence polynomials of zero-divisor graphs over commutative rings, focusing on the unimodality and log-concavity of their coefficient sequences and characterizing the distribution of their complex zeros. By integrating techniques from graph theory, algebraic combinatorics, polynomial analysis, and complex analysis, the work establishes the first proof that the independence polynomials of certain zero-divisor graphs satisfy the unimodality conjecture. It further demonstrates that the coefficient sequences for several classes of such graphs are both unimodal and log-concave, and rigorously proves that all zeros of these polynomials lie within a specific annular region in the complex plane. These results provide new structural insights into algebraic graph theory and the theory of combinatorial polynomials.

0 citationsRead paper

The NF-operator and the NF-Numbers of Simplicial Complexes

May 28, 2026

This study investigates the periodic behavior of simplicial complexes under iterated applications of the NF operator, defining the NF-number as the smallest positive integer for which the complex returns to an isomorphic state. By integrating Stanley–Reisner theory with structural analysis of facet ideals, the authors employ algebraic-combinatorial techniques to characterize the isomorphism classes along iteration orbits. Explicit formulas for the NF-number are established for the first time for dumbbell graphs, complete split graphs \(S_{n,m}\) (with NF-number \(n+m+2\)), and double star graphs \(D_{p,q}\) (with NF-number \(p+q+4\)). These results advance the interplay between combinatorial commutative algebra and graph theory and are accompanied by several open problems and conjectures.

0 citationsRead paper

Betti numbers for cochordal zero-divisor graphs of commutative rings

May 13, 2026

This study investigates homological invariants of zero-divisor graphs over finite chain rings, with a focus on the Betti numbers and algebraic properties of their edge ideals. By constructing a layered graph \( C(q,L) \) that encodes the zero-divisor structure, the authors prove that this graph is cochordal and thereby determine its type sequence, leading to a corrected and refined formula for the Betti numbers of the associated edge ideal. Employing techniques from combinatorial commutative algebra, cochordal graph theory, and homological algebra, they compute the projective dimension and Castelnuovo–Mumford regularity of Gaussian quotient rings \( \mathbb{Z}_{2^m}[i] \) and truncated polynomial rings \( \mathbb{Z}_p[x]/(x^c) \), establishing that these rings admit 2-linear resolutions. Moreover, they show that such rings are Cohen–Macaulay only in degenerate or complete graph cases.

0 citationsRead paper

Vertex connectivity of the nonzero nonunit core of the comaximal graph of $\mathbb Z_n$

May 02, 2026

This study investigates the vertex connectivity of the induced subgraph $G_2$, comprising nonzero non-units, in the comaximal graph of the ring $\mathbb{Z}_n$ where $n$ is square-free. By leveraging the Chinese Remainder Theorem to represent elements as coordinate vectors, $G_2$ is modeled as a weighted expansion of a set-disjointness graph. The authors precisely determine the vertex connectivity of $G_2$ to be $\prod_{i=1}^{m-1}(p_i - 1)$, thereby establishing that $G_2$ achieves maximal connectivity—equal to its minimum degree—and derive key structural properties including distance, diameter, and radius. Furthermore, they present a linear-time algorithm based on the prime factorization of $n$, which confirms the tightness of previously known upper bounds and affirms the optimal connectivity of this class of graphs.

0 citationsRead paper