Anita Pal

New concepts of fuzzy planar graphs

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

The F-coindex of some graph operations

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.

Modified Eccentric Connectivity of Generalized Thorn Graphs

The thorn graph of a given graph is obtained by attaching pendent vertices to each vertex of . The pendent edges, called thorns of , can be treated as or , so that a thorn graph is generalized by replacing by and by and the respective generalizations are denoted by and . The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivity index and the concerned polynomial for the thorn graph and the generalized thorn graphs and .

Some more results on fuzzy k-competition graphs

Fuzzy competition graph as the generalization of competition graph is introduced here. Fuzzy k-competition graph as a special type of fuzzy competition graph is defined here along with fuzzy isolated vertices. The fuzzy competition number is also introduced and investigated several properties. Isomorphism properties on fuzzy competition graphs are discussed.

Mitigating route request flooding attack in MANET using node reputation

An ad hoc network is an infrastructure-less, decentralized network, consisting of a group of mobile wireless nodes, moving around freely and cooperating with each other in routing and forwarding of packets. Due to the lack of any clear line of defense, MANET is accessible to both legitimate users and malicious attackers. Among various types of attacks, it is particularly vulnerable to various denial of service (DoS) attacks. Route request flooding attack is one such distributed DoS attack, launched by compromised nodes or intruders. This triggers an acute need of flooding attack prevention mechanisms for this highly vulnerable type of network. In this paper, a reputation based scheme is proposed to resist the impact of flooding attack in MANET. This scheme observes the behavior of a node in the network periodically and limits its route request sending rate accordingly.

The Fuzzy Robust Graph Coloring Problem

Fuzzy graph model can represent a complex, imprecise and uncertain problem, where classical graph model may fail. In this paper, we propose a fuzzy graph model to represent the examination scheduling problem of a university and introduce a genetic algorithm based method to find the robust solution of the scheduling problem that remains feasible and optimal or close to optimal for all scenarios of the input data. Fuzzy graph coloring method is used to compute the minimum number of days to schedule the examination. But problem arises if after the examination schedule is published, some students choose new courses in such a way that it makes the schedule invalid. We call this problem as fuzzy robust coloring problem (FRCP). We find the expression for robustness and based on its value, robust solution of the examination schedule is obtained. The concept of fuzzy probability of fuzzy event is used in the expression of robustness, which in turn, is used for fitness evaluation in genetic algorithm. Each chromosome in the genetic algorithm, used for FRCP, represents a coloring function. The validity of the coloring function is checked keeping the number of colors fixed. Fuzzy graphs with different number of nodes are used to show the effectiveness of the proposed method.

Incentive and Quality Aware Participatory Sensing System

Participatory Sensing system (PSS) is being thought of as an alternative model in the pervasive computing environment, to collect effective data from mobile human agents, where deployment of sensor agents to collect data will be costly. One of the main difficulties in collecting data from the human agents is that, they are not willing to participate in this data collecting process. Several incentive schemes, based on the framework of auction theory, are proposed to motivate the users to participate in this interesting data collection model. However none of the incentive schemes used to judge the quality of the users along with their bid prices to select the human agents. If the quality of the agents is used, the data collection model may attract the bidders with slightly higher valuation but providing a good quality data. This scheme will make the PSS more realistic. In this paper, an efficient scheme is proposed not only to motivate users but also to restrict manipulation in the bidding substantially. The simulation study shows that the proposed economic model can maintain better participation of the agents compared to the existing schemes and also it will perform better when the agents are rational.

On Some Bounds and Exact Formulae for Connective Eccentric Indices of Graphs under Some Graph Operations

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction, and splice of graphs.

Computing the Shortest path with Words

Computing with words is a soft computing technique to solve the decision-making problem with the information described in natural language. In this paper, we proposed a generalised Diskrtras algorithm for finding shortest paths from a source node to every other node in a fuzzy graph where the arc lengths are represented by some natural words taken from natural language. Human being generally describes the arc lengths of any shortest path problem in real life by the terms small, large, some, etc. term which do not supply any natural numbers or fuzzy numbers. We describe those terms as words. Here, we use interval type 2 fuzzy set (IT2FS) to capture the uncertainty of the words. A perceptual computer model is introduced to determine the rank of the shortest path which is a collection of words. A numerical example of transportation network is used to illustrate the effectiveness of the proposed method.

ECG Biometric Recognition

This paper presents a human recognition system using single lead electrocardiogram (ECG). The method corrects the ECG signal from noise as well as other artifacts to it and extracts major features from P-QRS-T waveforms. Finite Impulse Response (FIR) equiripple high pass filter is used for denoising ECG signal. Haar wavelet transform is used to detect the R peaks. By using this novel approach, different extensive information like heart rates, interval features, amplitude features, angle features area features are received among dominant fiducials of ECG waveform. The feasibility of ECG as a new biometric is tested on selected features that report the recognition accuracy to 97.12% on the data size of 100 recordings of PTB database. The results obtained from the proposed approach surpasses the other conventional methods for biometric applications.