Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

On the Spectra of Commuting and Non Commuting Graph on Dihedral Group

Abstract: Study about spectra of graph has became interesting work as well as study about commuting and non commuting graph of a group or a ring But the study about spectra of commuting and non commuting graph of dihedral group has not been done yet In this paper, we investigate adjacency spectrum, Laplacian spectrum, signless Laplacian spectrum, and detour spectrum of commuting and non commuting graph of dihedral group D 2 n

Hierarchical feature clustering for content-based retrieval in medical image databases

Abstract: In this paper we describe the construction of hierarchical feature clustering and show how to overcome general problems of region growing algorithms such as seed point selection and processing order. Access to medical knowledge inherent in medical image databases requires content-based descriptions to allow non-textual retrieval, e.g., for comparison, statistical inquiries, or education. Due to varying medical context and questions, data structures for image description must provide all visually perceivable regions and their topological relationships, which poses one of the major problems for content extraction. In medical applications main criteria for segmenting images are local features such as texture, shape, intensity extrema, or gray values. For this new approach, these features are computed pixel-based and neighboring pixels are merged if the Euclidean distance of corresponding feature vectors is below a threshold. Thus, the planar adjacency of clusters representing connected image partitions is preserved. A cluster hierarchy is obtained by iterating and recording the adjacency merging. The resulting inclusion and neighborhood relations of the regions form a hierarchical region adjacency graph. This graph represents a multiscale image decomposition and therefore an extensive content description. It is examined with respect to application in daily routine by testing invariance against transformation, run time behavior, and visual quality For retrieval purposes, a graph can be matched with graphs of other images, where the quality of the matching describes the similarity of the images.

Compact Data Structures for Temporal Graphs

Abstract: Summary form only given. In this paper we propose three compact data structures to answer queries on temporal graphs. We define a temporal graph as a graph whose edges appear or disappear along time. Possible queries are related to adjacency along time, for example, to get the neighbors of a node at a given time point or interval. A naive representation consists of a time-ordered sequence of graphs, each of them valid at a particular time instant. The main issue of this representation is the unnecessary use of space if many nodes and their connections remain unchanged during a long period of time. The work in this paper proposes to store only what changes at each time instant. The ttk2-tree is conceptually a dynamic k2-tree in which each leaf and internal node contains a change list of time instants when its bit value has changed. All the change lists are stored consecutively in a dynamic sequence. During query processing, the change lists are used to expand only valid regions in the dynamic k2-tree. It supports updates of the current or past states of the graph. The ltg-index is a set of snapshots and logs of changes between consecutive snapshots. The structure keeps a log for each node, storing the edge and the time where a change has been produced. To retrieve direct neighbors of a node, the previous snapshot is queried, and then the log is traversed adding or removing edges to the result. The differential k2-tree stores snapshots of some time instants in k2-trees. For the other time instants, a k2-tree is also built, but these are differential (they store the edges that differ from the last snapshot). To perform a query it accesses the k2-tree of the given time and the previous full snapshot. The edges that appear in exactly one of these two k2-trees will be the final results. We test our proposals using synthetic and real datasets. Our results show that the ltg-index obtains the smallest space in general. We also measure times for direct and reverse neighbor queries in a time instant or a time interval. For all these queries, the times of our best proposal range from tens of μs to several ms, depending on the size of the dataset and the number of results returned. The ltg-index is the fastest for direct queries (almost as fast as accessing a snapshot), but it is 5-20 times slower in reverse queries. The differential k2-tree is very fast in time instant queries, but slower in time interval queries. The ttk2-tree obtains similar times for direct and reverse queries and different time intervals, being the fastest in some reverse interval queries. It has also the advantage of being dynamic.

Segmentation of range images into planar regions

Abstract: This paper presents a hybrid approach to the segmentation of range images into planar regions. The term hybrid refers to a combination of edge- and region-based considerations. A reliable computational procedure which takes the range image discontinuities into account is presented for computing the pixel's normal. The segmentation algorithm consists of two parts. In the first one, the pixels are aggregated according to local properties derived from the input data and are represented by a region adjacency graph (RAG). At this stage, the image is still over-segmented. In the second part, the segmentation is refined thanks to the construction of an irregular pyramid. The base of the pyramid is the RAG previously extracted. The over-segmented regions are merged using a surface-based description. This algorithm has been evaluated on 80 real images acquired by two different range sensors using the methodology proposed in (Hoover et al., 1996). Experimental results are presented and compared to others obtained by four research groups.

Adjacency matrices of polarity graphs and of other C4-free graphs of large size

Abstract: In this paper we give a method for obtaining the adjacency matrix of a simple polarity graph G q from a projective plane PG(2, q), where q is a prime power. Denote by ex(n; C 4) the maximum number of edges of a graph on n vertices and free of squares C 4. We use the constructed graphs G q to obtain lower bounds on the extremal function ex(n; C 4), for some n < q 2 + q + 1. In particular, we construct a C 4-free graph on $${n=q^2 -\sqrt{q}}$$ vertices and $${\frac{1}{2} q(q^2-1)-\frac{1}{2}\sqrt{q} (q-1) }$$ edges, for a square prime power q.