207130305
On k-pairable graphs
Motivated by a 1994 result of Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) about spanning trees of the graphs with an antipodal isomorphism, we introduce the concept of k-pairable graphs and extend the result in Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) to this larger class of graphs. We then define a new graph parameter p(G), called the pair length of graph G. This parameter measures the maximum distance, in some sense, between a subgraph induced by half the vertices of G with the isomorphic subgraph induced by the other half of V(G). An upper bound for the parameter p(G) is given. Some properties of the k-pairable graphs and their product graphs are studied. We also post some problems for further research.
1865477
On integral sum graphs
A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u)+f(v)=f(w) for some node w in G. A node of G is called a saturated node if it is adjacent to every other node of G. We show that any integral sum graph which is not K"3 has at most two saturated nodes. We determine the structure for all integral sum graphs with exactly two saturated nodes, and give an upper bound for the number of edges of a connected integral sum graph with no saturated nodes. We introduce a method of identification on constructing new connected integral sum graphs from given integral sum graphs with a saturated node. Moreover, we show that every graph is an induced subgraph of a connected integral sum graph. Miscellaneous related results are also presented.
10941860
Fan-Type Conditions for Collapsible Graphs
A graph G is collapsible if for every even subset R <;; V ( G), there is a spanning connected subgraph of G whose set of odd degree vertices is R. A graph is supereulerian if it contains a spanning closed trail. It is known that every collapsible graph is supereulerian. A graph G of order n is said to satisfy a Fan­ type condition if max{d(u),d(v)} 2: n/(g 2)p E for each pair of vertices u, v at distance two1 where g E {3, 4} is the girth of G, and p 2: 2 and , 2: 0 are fixed numbers. In this paper, we study the Fan-type conditions for collapsible graphs and supereulerian graphs.
14132390
Log mining to improve the performance of site search
Despite of the popularity of global search engines,people still suffer from low accuracy of site search. Theprimary reason lies in the difference of link structuresand data scale between global Web and website, whichleads to failures of traditional re-ranking methods suchas HITS, PageRank and DirectHit. This paper proposes anovel re-ranking method based on user logs withinwebsites. With the help of website taxonomy, we mine forgeneralized association rules and abstract accesspatterns of different levels. Mining results aresubsequently used to re-rank the retrieved pages. One ofthe advantages of our mining algorithm is that it resolvesthe diversity problem of user's access behavior anddiscovers general patterns. Experiment shows that theproposed method outperforms keyword-based method by15% and DirectHit by 13% respectively.
86627129
Identification of business forms using relationships between adjacent frames
This paper proposes a method of using relationships between adjacent frames to identify business forms. First, we use the relations between adjacent frames in the business form to represent each form as two graphs. We then convert these graphs to two 1-D strings, which are used to perform matching. This approach enables forms to be identified quickly, and it places no restrictions on the layout of the business forms.
30786237
Spanning closed trails in graphs
Abstract Let G be a 2-edge-connected simple graph on n >;95 vertices. Let l be the number of vertices of degree 2 in G . We prove that if l n ⧸5−19 and if, for every edge uvϵE ( G ), d ( v )+ d ( v )⩾2 n ⧸5−2, then exactly one of the following holds: (a) G has a spanning closed trail; (b) G can be contracted to K 2, c −2 , where c ⩽ max {5, 3+ l } is an odd number. An example shows that if a graph satisfies the conditions above except that it has too many vertices of degree 2, then the conclusion fails. This result is related to a conjecture of Benhocine et al. (1986), recently proved by Veldman. We obtain some other related results.
1830855
Web mining for Web image retrieval
The popularity of digital images is rapidly increasing due to improving digital imaging technologies and convenient availability facilitated by the Internet. However, how to find user-intended images from the Internet is non-trivial. The main reason is that the web images are usually not annotated using semantic descriptors. In this paper, we present an effective approach to and a prototype system for image retrieval from the Internet using web mining. The system can also serve as a web image search engine. One of the key ideas in the approach is to extract the text information on the web pages to semantically describe the images. The text description is then combined with other low-level image features in the image similarity assessment. Another main contribution of this work is that we apply data mining on the log of user’s feedback to improve image retrieval performance in three aspects: First, the accuracy of the document space model of image representation obtained from the web pages is improved by removing clutter and irrelevant text information; Second, to construct the user space model of users’ representation of images, which is then combined with the document space model to eliminate mismatch between the page author’s expression and the user’s understanding and expectation; Third, to discover the relationship between low-level and high-level features, which is extremely useful for assigning the low-level features’ weights in similarity assessment.