31147226
On felicitous graphs
Abstract A graph with n edges is called harmonious if it is possible to label the vertices with distinct numbers (modulo n ) in such a way that the edge labels which are sums ofend-vertex labels are also distinct (modulo n ). A generalization of harmonious graphs is felicitous graphs. In felicitous labelling distinct numbers (modulo n + 1) are used to label the vertices of a graph with n edges so that the edge labels are distinct (modulo n ). We give some necessary conditions for a graph to be felicitous. Some families of graphs (cycles of order 4 k , complete bipartite graphs, generalized Petersen graphs,…) are shown to be felicitous, while others (cycles of order 4 k + 2, the complete graph K itn when n ⩾5…) arenot. We also find that almost all graphs are not felicitous.
6805642
Uniformly cordial graphs
Let G be a graph with vertex set V(G) and edge set E(G). A labeling f:V(G)->{0,1} induces an edge labeling f^*:E(G)->{0,1}, defined by f^*(xy)=|f(x)-f(y)| for each edge [email protected]?E(G). For [email protected]?{0,1}, let n"i(f)=|{[email protected]?V(G):f(v)=i}| and m"i(f)=|{[email protected]?E(G):f^*(e)=i}|. Let c(f)=|m"0(f)-m"1(f)|. A labeling f of a graph G is called friendly if |n"0(f)-n"1(f)|= =2 is uniformly cordial if and only if n=3 and G=K"3, or n is even and G=K"1","n"-"1.
5645473
On Magic Strength of Graph
35676657
On skolem graceful graphs
Abstract A Skolem graceful labelling of graphs is introduced. It is shown that a tree is Skolem graceful iff it is graceful. The Skolem deficiency of a graph is defined and Skolem deficiencies of some well-known graphs are calculated. The class of Skolem graceful graphs is shown to be finite universal.
650244
IC-Colorings and IC-Indices of graphs
Given a coloring f:V(G)->N of graph G and any subgraph H@?G we define f"s(H)=@?"v"@?"V"("H")f(v). In particular, we denote f"s(G) by S(f). The coloring f is called an IC-coloring if for any integer k@?[1,S(f)] there is a connected subgraph H@?G such that f"s(H)=k. Also, we define the IC-index of G to beM(G)=max{S(f):f is an IC-coloring of G}.In this paper we examine some well-known classes of graphs and determine their IC-indices. In addition, several conjectures are proposed.
9314363
Feature sensitive mesh segmentation with mean shift
Feature sensitive mesh segmentation is important for many computer graphics and geometric modeling applications. In this paper, we develop a mesh segmentation method, which is capable of producing high-quality shape partitioning. It respects fine shape features and works well on various types of shapes, including natural shapes and mechanical parts. The method combines a procedure for clustering mesh normals with a modification of the mesh clarification technique. For clustering of mesh normals, we adopt Mean Shift, a powerful general purpose technique for clustering scattered data. We demonstrate advantages of our method by comparing it with two state-of-the-art mesh segmentation techniques.
8239327
A filter bank approach to independent component analysis for convolved mixtures
Abstract We present a filter bank approach to perform independent component analysis (ICA) for convolved mixtures. Input signals are split into subband signals and subsampled. A simplified network performs ICA on the subsampled signals, and finally independent components are synthesized. The proposed approach achieves superior performance than the frequency domain approach and faster convergence with less computational complexity than the time domain approach. Furthermore, it requires shorter unmixing filter length and less computational complexity than other filter bank approaches by designing efficient filter banks. Also, a method is proposed to resolve the permutation and scaling problems of the filter bank approach.
11512918
Combining Source- and Localized Recovery to Achieve Reliable Multicast in Multi-hop Ad Hoc Networks
This paper proposes a novel reliable multicast transport protocol for multi-hop, wireless ad hoc networks (or MANETs). To recover from the different types of losses that may occur in MANETs, our Reliable Adaptive Congestion-controlled Transport protocol, or Re-ACT, combines source-based congestion- and error control with receiver-initiated localized recovery. While the latter attempts to recover localized losses (e.g., caused by transmission errors), the former is invoked only for losses and congestion that could not be recovered locally (e.g., caused by global congestion). Loss differentiation is an important component of ReACT and uses medium access control (MAC) layer information to distinguish between different types of losses. Through extensive simulations, we evaluate ReACT’s performance under a variety of MANET scenarios, including different offered load and mobility conditions, and compare it against a strictly end-to-end (i.e., no localized recovery) scheme. Our results show that ReACT is the best performer in terms of reliability. Our results also showcase the effect of ReACT’s local recovery mechanism which quickly corrects error- and path breakage induced losses and thus manages to prevent the source from reducing its rate unnecessarily , thus achieving significant throughput improvement with lower overhead when compared to the strictly end-to-end protocol.
232491
Transitive Mesh Space of a Progressive Mesh
The paper investigates the set of all selectively refined meshes that can be obtained from a progressive mesh. We call the set the transitive mesh space of a progressive mesh and present a theoretical analysis of the space. We define selective edge collapse and vertex split transformations, which we use to traverse all selectively refined meshes in the transitive mesh space. We propose a complete selective refinement scheme for a progressive mesh based on the transformations and compare the scheme with previous selective refinement schemes in both theoretical and experimental ways. In our comparison, we show that the complete scheme always generates selectively refined meshes with smaller numbers of vertices and faces than previous schemes for a given refinement criterion. The concept of dual pieces of the vertices in the vertex hierarchy plays a central role in the analysis of the transitive mesh space and the design of selective edge collapse and vertex split transformations.
15970244
Truly Selective Refinement of Progressive Meshes
This paper presents a novel selective refinement scheme of progressive meshes. In previous schemes, topology information in the neighborhood of a collapsed edge is stored in the analysis phase. A vertex split or edge collapse transformation is possible in the synthesis phase only if the configuration of neighborhood vertices in the current mesh corresponds to the stored topology information. In contrast, the proposed scheme makes it possible to apply a vertex split or an edge collapse to any selected vertex or edge in the current mesh without a precondition. Our main observation is that the concept of a dual piece can be used to clearly enumerate and visualize the set of all possible selectively refined meshes for a given mesh. Our refinement scheme is truly selective in the sense that each vertex split or edge collapse can be performed without incurring additional vertex split and/or edge collapse transformations.