Integral Distance Graphs

نویسندگان

Jer-Jeong Chen

Gerard J. Chang

Kuo-Ching Huang

چکیده

Suppose D is a subset of all positive integers. The distance graph G(Z,D) with distance set D is the graph with vertex set Z, and two vertices x and y are adjacent if and only if |x− y| ∈ D. This paper studies the chromatic number χ(Z,D) of G(Z,D). In particular, we prove that χ(Z,D) ≤ |D|+1 when |D| is finite. Exact values of χ(G,D) are also determined for some D with |D| = 3. c © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 287–294, 1997

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the distance eigenvalues of Cayley graphs

In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...

متن کامل

Distance spectra and Distance energy of Integral Circulant Graphs

The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the ...

متن کامل

On distance integral graphs

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D, and they form the distance spectrum of G. A graph is called distance integral if its distance spectrum consists entirely of integers. We show that no nontrivial tree can be distance integral. We characterize distance integral graphs in the classes of graphs similar to complete split graphs, which, toge...

متن کامل

Matching Integral Graphs of Small Order

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

متن کامل

Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups

It is shown that distance powers of an integral Cayley graph over an abelian group Γ are again integral Cayley graphs over Γ. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum.

متن کامل