the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 26 (2010) 95--105‎.]. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

the divisibility graph $mathscr{d}(g)$ for a finite group $g$ is a graph with vertex set ${rm cs}(g)setminus{1}$‎ ‎where ${rm cs}(g)$ is the set of conjugacy class sizes of $g$‎. ‎two vertices $a$ and $b$ are adjacent whenever $a$ divides‎ ‎$b$ or $b$ divides $a$‎. ‎in this paper we will find the number of connected components of $mathscr{d}(g)$ where $g$ is a‎ ‎simple zassenhaus group or an sp...

Word spotting is to make searchable unindexed image documents by locating word/words in a doc-ument image, given a query word. This problem is challenging, mainly due to the large numberof word classes with very small inter-class and substantial intra-class distances. In this paper, asegmentation-based word spotting method is presented for multi-writer Persian handwritten doc-...

A new class of Gibbsian models with potentials associated to the connected components or homogeneous parts of images is introduced. For these models the neighbourhood of a pixel is not fixed as for Markov random fields, but given by the components which are adjacent to the pixel. The relationship to Markov random fields and marked point processes is explored and spatial Markov properties are es...

Article history: Received 27 March 2008 Received in revised form 2 September 2008 Accepted 20 October 2008

a. csaszar introduced and extensively studied the notion of generalized opensets. following csazar, we introduce a new notion hyperconnected. we study some speci cproperties about connected and hyperconnected in generalized topological spaces. finally, wecharacterize the connected component in generalized topological spaces.

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...