منابع مشابه
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 کاملIntegral Distance Graphs
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 Wi...
متن کاملRemarks on Distance-Balanced Graphs
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کاملDistance 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 کاملOn 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.03.004