若干类满足■dm猜想的循环图

本文对阶数为素数幂n=p^n的循环图,讨论了它关于Adam同构的问题。对于无向循环图G_n(K),其中K={a_i,n-a_i|0<a_i<n-a_i,i=1,2,…,k}且k≤p,证明了G_n(K)满足Adam猜想。本文还构造了一类同构但不满足Adam猜想的循环图,从而说明对于素数幂这里得到的结果是最好的。此外,还得到了另外几类满足Adam猜想的循环图,并且讨论了循环图的补图的Adam同构性质。

A Note on Strongly Regular Self-complementary Graphs

Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.

Autonomous map query:robust visual localization in urban environments using Multilayer Feature Graph

When a vehicle travels in urban areas, onboard global positioning system （GPS） signals may be obstructed by high-rise buildings and thereby cannot provide accurate positions. It is proposed to perform localization by registering ground images to a 2D building boundary map which is generated from aerial images. Multilayer feature graphs （MFG） is employed to model building facades from the ground images. MFG was reported in the previous work to facilitate the robot scene understand- ing in urhan areas. By constructing MFG, the 2D/3D positions of features can be obtained, inclu- cling line segments, ideal lines, and all primary vertical planes. Finally, a voting-based feature weighted localization method is developed based on MFGs and the 2D building boundary map. The proposed method has been implemented and validated in physical experiments. In the proposed ex- periments, the algorithm has achieved an overall localization accuracy of 2.2m, which is better than commercial GPS working in open environments.

Determination of Wood Moisture Properties Using a CT-Scanner in a Controlled High-Temperature Environment

Theaim of the present work wasto analyze moisture flow and moisture content data for high-temperature drying by usingan advanced image- processing algorithm.Since wood starts to shrink below the fibre saturation point during drying, the size and shape of wood will change. The dry wood image was thoroughly transformed to the shape of the wet wood image prior to calculating the dry weight moisture content. The use of the image- processing algorithm for the dry weight moisture content on density data from the CT-scanning during drying in a controlled high-temperature environment showed that this method is a powerful tool for analyzing the moisture flow inside the wood piece. Furthermore, the new CT-scanner together with the climate chamber gave unique results, as it has not been possible to study high-temperature drying with this method before.

Acyclic improper colouring of graphs with maximum degree 4

A k-colouring （not necessarily proper） of vertices of a graph is called acyclic, if for every pair of distinct colours i and j the subgraph induced by the edges whose endpoints have colours i and j is acyclic. We consider acyclie k-eolourings such that each colour class induces a graph with a given （hereditary） property. In particular, we consider aeyclic k-eolourings in which each colour class induces a graph with maximum degree at most t, which are referred to as acyclic t-improper k-colourings. The acyelic t-improper chromatic number of a graph G is the smallest k for which there exists an acyclic t-improper k-colouring of G. We focus on acyclic colourings of graphs with maximum degree 4. We prove that 3 is an upper bound for the acyclic 3-improper chromatic number of this class of graphs. We also provide a non-trivial family of graphs with maximum degree 4 whose acyclic 3-improper chromatic number is at most 2, namely, the graphs with maximum average degree at most 3. Finally, we prove that any graph G with A（G） ≤ 4 can be acyelically coloured with 4 colours in such a way that each colour class induces an acyclic graph with maximum degree at most 3.