Distance monotonicity and a new characterization of hypercubes
نویسندگان
چکیده
In this paper, we are interested in some metric properties of graphs. In particular, we investigate distance monotonicity in graphs. Straightaway, we revisit the notion of distance monotonicity. We then introduce interval distance monotone graphs, graphs which are not distance monotone but whose intervals are distance monotone. Finally, we obtain a new characterization of hypercubes involving this notion. c © 2002 Elsevier Science B.V. All rights reserved.
منابع مشابه
A characterization of the interval distance monotone graphs
A simple connected graph G is said to be interval distance monotone if the interval I (u, v) between any pair of vertices u and v in G induces a distance monotone graph. Aïder and Aouchiche [Distance monotonicity and a new characterization of hypercubes, Discrete Math. 245 (2002) 55–62] proposed the following conjecture: a graph G is interval distance monotone if and only if each of its interva...
متن کاملProduct-closed networks
We present a uniform mathematical characterization of interconnection network classes referred to as product-closed networks (PCN). A number of popular network classes fall under this characterization including binary hypercubes, tori, k-ary n-cubes, meshes, and generalized hypercubes. An unlimited number of other networks can be defined using the presented mathematical characterization. An imp...
متن کاملThe Geometry of Sets of Orthogonal Frequency Hypercubes
We extend the notion of a framed net, introduced by D. Jungnickel, V.C. Mavron, and T.P. McDonough in The geometry of frequency squares, J. Combinatorial Theory A, 96 (2001), 376–387, to that of a d-framed net of type `, where d ≥ 2 and 1 ≤ ` ≤ d − 1, and we establish a correspondence between d-framed nets of type ` and sets of mutually orthogonal frequency hypercubes of dimension d. We provide...
متن کاملProperty testing for distributions on partially ordered sets
We survey the results of Rubinfeld, Batu et al. ([2], [3]) on testing distributions for monotonicity, and testing distributions known to be monotone for uniformity. We extend some of their results to new partial orders, and provide evidence for some new conjectural lower bounds. Our results apply to various partial orders: bipartite graphs, lines, trees, grids, and hypercubes. Thesis Supervisor...
متن کاملMonotonicity Testing and Shortest-Path Routing on the Cube
We study the problem of monotonicity testing over the hypercube. As previously observed in several works, a positive answer to a natural question about routing properties of the hypercube network would imply the existence of efficient monotonicity testers. In particular, if any ` disjoint source-sink pairs on the directed hypercube can be connected with edge-disjoint paths, then monotonicity of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 245 شماره
صفحات -
تاریخ انتشار 2002