Let G be a simple graph of order n and size m. An edge covering of a graph is a set of edges
such that every vertex of the graph is incident to at least one edge of the set. In this paper we …

We use Wagner's weighted subgraph counting polynomial to prove that the partition function
of the anti-ferromagnetic Ising model on line graphs is real rooted and to prove that roots of …

Let G be a graph of order n. A dominating set of G is a subset of vertices of G, say S, such
that every vertex in V (G)∖ S is adjacent to at least one vertex of S. The domination …

Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial,
the matching polynomial, and many others are widely studied. In this paper we examine to …

In this article, we study problems where one has to prove that certain graph parameter
attains its maximum at the star and its minimum at the path among the trees on a fixed …

We present fully polynomial time approximation schemes for a broad class of Holant
problems with complex edge weights, which we call Holant polynomials. We transform these …

Graph polynomials are graph parameters invariant under graph isomorphisms which take
values in a polynomial ring with a fixed finite number of indeterminates. We study graph …

Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-
adjacent vertices. The independence polynomial of G is the polynomial …

The independence polynomial of a graph is the generating polynomial for the number of
independent sets of each size and its roots are called independence roots. We bound the …

本文根据不同图形的特点, 通过递归的方法研究并给出了它们的边覆盖多项式,
并进一步研究了这些多项式的对数凹性, 主要包括蜈蚣图, 毛虫图, 脊椎图, 爆竹图等图. Abstract …