On Circulants Uniquely Characterized by their Independence Polynomials
نویسندگان
چکیده
In [18], Farrell and Whitehead investigate circulant graphs that are uniquely characterized by their matching and chromatic polynomials (i.e., graphs that are “matching unique” and “chromatic unique”). They develop a partial classification theorem, by finding all matching unique and chromatic unique circulants on n vertices, for each n ≤ 8. In this paper, we explore circulant graphs that are uniquely characterized by their independence polynomials. We obtain a full classification theorem by proving that a circulant is independence unique iff it is the disjoint union of isomorphic complete graphs.
منابع مشابه
Independence polynomials of circulants with an application to music
The independence polynomial of a graph G is the generating function I(G, x) = ∑ k≥0 ikx k, where ik is the number of independent sets of cardinality k in G. We show that the problem of evaluating the independence polynomial of a graph at any fixed non-zero number is intractable, evenwhen restricted to circulants. We provide a formula for the independence polynomial of a certain family of circul...
متن کاملWell-covered circulant graphs
A graph is well-covered if every independent set can be extended to a maximum independent set. We show that it is co-NP-complete to determine whether an arbitrary graph is well-covered, even when restricted to the family of circulant graphs. Despite the intractability of characterizing the complete set of well-covered circulant graphs, we apply the theory of independence polynomials to show tha...
متن کاملRAPPORT Primes in the doubly stochastic circulants
The algebraic structure of the set of doubly stochastic circulants is that of a semi-ring. The concept of a prime in the doubly stochastic circulants is introduced in this paper and examples are given. The classiication of a prime in the doubly stochastic circulants is equivalent to the solvability of a linear equation over a doubly stochastic circulant. A representation of doubly stochastic ci...
متن کاملON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS
Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...
متن کاملOn the independence polynomial of an antiregular graph
A graph with at most two vertices of the same degree is called antiregular [25], maximally nonregular [32] or quasiperfect [2]. If sk is the number of independent sets of cardinality k in a graph G, then I(G;x) = s0 + s1x+ ...+ sαx α is the independence polynomial of G [10], where α = α(G) is the size of a maximum independent set. In this paper we derive closed formulae for the independence pol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ars Comb.
دوره 104 شماره
صفحات -
تاریخ انتشار 2012