F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds

This paper proves the existence of face antimagic labeling for double duplication of barycentric subdivision of cycle and some other graphs 

Our active aim in this paper is to prove the following Let Ŕ be a ring having an
idempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ which
satisfies:
(i) eR  R and Re  R .
(ii) xR  0 implies x  0 .
(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .
(iv) exeR(1 e)  0 implies exe  0 .
If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D is
additive. This extend Daif's result to the case R need not contain any non-zero
idempotent element.

A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .

A super pixel can be defined as a group of pixels, which have similar characteristics, which can be very helpful for image segmentation. It is generally color based segmentation as well as other features like texture, statistics…etc .There are many algorithms available to segment super pixels like Simple Linear Iterative Clustering (SLIC) super pixels and Density-Based Spatial Clustering of Application with Noise (DBSCAN). SLIC algorithm essentially relay on choosing N random or regular seeds points covering the used image for segmentation. In this paper Split and Merge algorithm was used instead to overcome determination the seed point's location and numbers as well as other used parameters. The overall results were better from the SL

The road network serves as a hub for opportunities in production and consumption, resource extraction, and social cohabitation. In turn, this promotes a higher standard of living and the expansion of cities. This research explores the road network's spatial connectedness and its effects on travel and urban form in the Al-Kadhimiya and Al-Adhamiya municipalities. Satellite images and paper maps have been employed to extract information on the existing road network, including their kinds, conditions, density, and lengths. The spatial structure of the road network was then generated using the ArcGIS software environment. The road pattern connectivity was evaluated using graph theory indices. The study demands the abstractio

The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .

     The result involution graph of a finite group , denoted by  is an undirected simple graph whose vertex set is the whole group  and two distinct vertices are adjacent if their product is an involution element. In this paper, result involution graphs for all Mathieu groups and connectivity in the graph are studied. The diameter, radius and girth of this graph are also studied. Furthermore, several other graph properties are obtained.

A network (or formally a graph) can be described by a set of nodes and a set of edges connecting these nodes. Networks model many real-world phenomena in various research domains, such as biology, engineering and sociology. Community mining is discovering the groups in a network where individuals group of membership are not explicitly given. Detecting natural divisions in such complex networks is proved to be extremely NP-hard problem that recently enjoyed a considerable interest. Among the proposed methods, the field of evolutionary algorithms (EAs) takes a remarkable interest. To this end, the aim of this paper is to present the general statement of community detection problem in social networks. Then, it visits the problem as an optim

     This paper describes the application of consensus optimization for Wireless Sensor Network (WSN) system. Consensus algorithm is usually conducted within a certain number of iterations for a given graph topology. Nevertheless, the best Number of Iterations (NOI) to reach consensus is varied in accordance with any change in number of nodes or other parameters of . graph topology. As a result, a time consuming trial and error procedure will necessary be applied
to obtain best NOI. The implementation of an intellig ent optimization can effectively help to get the optimal NOI. The performance of the consensus algorithm has considerably been improved by the inclusion of Particle Swarm Optimization (PSO). As a case s