4 citations · 20 across the 32 of their papers we have counts for
24 papers · 1 filter
Two conjectures on graphs and their edge-path matrices
Metrose Metsidik, Xian'an Jin
The edge-path matrix is a square matrix where each off-diagonal entry records the maximum number of edge-disjoint paths between the corresponding pair of vertices. Akbari et al. [O…
A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Tamás Kálmán
The Tutte polynomial is a fundamental invariant of matroids. The polymatroid Tutte polynomial , introduced by Bernardi, Kálmán, and Postnikov, is an extension…
Extreme coefficients of multiplicity Tutte polynomials
Xian'an Jin, Tianlong Ma, Weiling Yang
The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an ex…
Two spectral extremal results for graphs with given order and rank
Xiuqing Li, Xian'an Jin, Chao Shi +1
The spectral radius and rank of a graph are defined to be the spectral radius and rank of its adjacency matrix, respectively. It is an important problem in spectral extremal graph…
Partial-twuality polynomials of delta-matroids
Qi Yan, Xian'an Jin
Gross, Mansour and Tucker introduced the partial-twuality polynomial of a ribbon graph. Chumutov and Vignes-Tourneret posed a problem: it would be interesting to know whether the p…
On the polymatroid Tutte polynomial
Xiaxia Guan, Weiling Yang, Xian'an Jin
The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial , introduced by Bernardi et al., is an extension of the classic…
Twist monomials of binary delta-matroids
Qi Yan, Xian'an Jin
Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials have only one term and pose…
On coefficients of the interior and exterior polynomials
Xiaxia Guan, Xian'an Jin
The interior polynomial and the exterior polynomial are generalizations of valuations on and of the Tutte polynomial of graphs to hypergraphs, respec…
A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs
Xiaxia Guan, Xian'an Jin, Tianlong Ma
T. Kálmán (A version of Tutte's polynomial for hypergraphs, Adv. Math. 244 (2013) 823-873.) introduced the interior and exterior polynomials which are generalizations of the Tutte…
Twist polynomials of delta-matroids
Qi Yan, Xian'an Jin
Recently, Gross, Mansour and Tucker introduced the partial duality polynomial of a ribbon graph and posed a conjecture that there is no orientable ribbon graph whose partial dualit…
The Ihara-zeta function and the spectrum of the join of two semi-regular bipartite graphs
Xiaotong Li, Xian'an Jin, Qi Yan
In this paper, using matrix techniques, we compute the Ihara-zeta function and the number of spanning trees of the join of two semi-regular bipartite graphs. Furthermore, we show t…
Tutte polynomials of fan-like graphs with applications in benzenoid systems
Tianlong Ma, Xian'an Jin, Fuji Zhang
We study the computation of the Tutte polynomials of fan-like graphs and obtain expressions of their Tutte polynomials via generating functions. As applications, Tutte polynomials,…
Partial-dual genus polynomials and signed intersection graphs
Qi Yan, Xian'an Jin
Recently, Gross, Mansour and Tucker introduced the partial-dual genus polynomial of a ribbon graph as a generating function that enumerates the partial duals of the ribbon graph by…
Counterexamples to the interpolating conjecture on partial-dual genus polynomials of ribbon graphs
Qi Yan, Xian'an Jin
Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They showed that the partial-dual genus polynomial fo…
Excluded checkerboard colourable ribbon graph minors
Xia Guo, Xian'an Jin, Qi Yan
In this paper, we first introduce the notions of checkerboard colourable minors for ribbon graphs motivated by the Eulerian ribbon graph minors, and two kinds of bipartite minors f…
Counterexamples to conjectures by Gross, Mansour and Tucker on partial-dual genus polynomials of ribbon graphs
Qi Yan, Xian'an Jin
Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They computed these two partial-dual genus polynomial…
Eulerian and bipartite binary delta-matroids
Qi Yan, Xian'an Jin
Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is bipartite if and only if its Petrie…
Characterization of regular checkerboard colourable twisted duals of ribbon graphs
Xia Guo, Xian'an Jin, Qi Yan
The geometric dual of a cellularly embedded graph is a fundamental concept in graph theory and also appears in many other branches of mathematics. The partial dual is an essential…
Checkerboard colourable twisted duals
Qi Yan, Xian'an Jin
In this note we show that any embedded graph has a checkerboard colourable twisted dual and any Eulerian embedded graph has a checkerboard colourable partial Petrial, answering que…
Characterizations of Eulerian and even-face partial duals of ribbon graphs
Qingying Deng, Xian'an Jin
Huggett and Moffatt characterized all bipartite partial duals of a plane graph in terms of all-crossing directions of its medial graph. Then Metsidik and Jin characterized all Eule…
Several extreme coefficients of the Tutte polynomial of graphs
Helin Gong, Mengchen Li, Xian'an Jin
Let be the coefficient of in the Tutte polynomial of a connected bridgeless and loopless graph with order and size . It is trivial that $t_…
A formula for the number of the spanning trees of line graphs
Helin Gong, Xian'an Jin
Let be a loopless graph and be the set of all spanning trees of . Let be the line graph of the graph and be the number of spannin…
A relationship between two graphical models of the Kauffman polynomial
Xian'an Jin
There are two oriented 4-valent graphical models for the Kauffman polynomial: one (HJ) is obtained by combining Jaeger's formula and Kauffman-Vogel model for the Homflypt polynomia…
The replacements of signed graphs and Kauffman brackets of links
Xian'an Jin, Fuji Zhang
Let be a signed graph. Let be the graph obtained from by replacing each edge by a chain or a sheaf. We first establish a relation between the -polynomial o…