Dr. Anita Pal | National Institute of Technology, Durgapur (original) (raw)

Papers by Dr. Anita Pal

arXiv (Cornell University), Jun 2, 2014

The connective eccentric index of a graph is a topological index involving degrees and eccentrici... more 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.

Finding shortest paths in graphs has been the area of interest for many researchers. Shortest pat... more Finding shortest paths in graphs has been the area of interest for many researchers. Shortest paths are one of the fundamental and most widely used concepts in networks. In this paper the authors present an algorithm to find an Intuitionistic Fuzzy Shortest Path (IFSP) in a directed graph in which the cost of every edges are represented by a trapezoidal intuitionistic fuzzy numbers(TrIFNs) which is the most generalized form of Trapezoidal Fuzzy Numbers(TrFNs) consisting of degree of acceptance and degree of rejection. The proposed algorithm uses Induced Intutionistic Trapezoidal Fuzzy Order Weighted Geometric (I-ITFOWG) operator for finding Intuitionistic Fuzzy Shortest Path (IFSP). A numerical example is given to explain the proposed algorithm.

Abstract. Let G = (V,E,σ,µ) be a simple connected undirected fuzzy graph. In this paper, we use a... more Abstract. Let G = (V,E,σ,µ) be a simple connected undirected fuzzy graph. In this paper, we use a fuzzy graph model to represent a traffic network of a city and discuss a method to find the different type of accidental zones in a traffic flows. Depending on the possibility of accident, this paper classifies accidental zone of a traffic flow into three type’s namely α-strong, β-strong and δ-strong accidental zones. The advantage of this type of classifications is that it helps to minimize the accident. We also discuss two different approaches of fuzzy graph coloring for solving two major problems in traffic control. First approach is based on fuzzy coloring of fuzzy graphs and fuzziness of vertices. Using this approach, we can minimize the total waiting time of a traffic flow. It will help to reduce the traffic jam of a road. Second approach is based on the vertex coloring function of a fuzzy graph (crisp mode). The function is based on α cut of graph Gα=(Vα,Eα),the α cuts of fuzzy g...

International Journal of Mathematics for Industry, 2020

A graph is a mathematical model used to predict the topology of a given system. In chemical graph... more A graph is a mathematical model used to predict the topology of a given system. In chemical graph theory, a graph is designed by considering atoms as vertices and edges as bonds between atoms of a particular molecule. A topological index or molecular structure descriptor is a numeric quantity associated with the chemical constitution which correlated with various physiochemical properties of the chemical structure. In this paper, we study the [Formula: see text]-Zagreb index of line graphs of the subdivision graphs of some chemical structures.

Abstract. A (2,1)-total labelling of a graph is an assignment of integers to each vertex and edge... more Abstract. A (2,1)-total labelling of a graph is an assignment of integers to each vertex and edge such that: (i) any two adjacent vertices of G receive distinct integers, (ii) any two adjacent edges of G receive distinct integers, and (iii) a vertex and its incident edge receive integers that differ by at least 2. The span of a (2,1)-total labelling is the maximum difference between two labels. The minimum span of a (2,1)total labelling of G is called the (2,1)-total number and denoted by . = ( , ) G V E

Journal of Advances in Mathematics, 2015

Journal of Molecular Structure, 2021

There is powerful relation between the chemical behaviour of chemical compounds and their molecul... more There is powerful relation between the chemical behaviour of chemical compounds and their molecular structures. Topological indices defined on these chemical molecular structures are capable to predict physical properties, chemical reactivity and biological activity. In this article, a new topological index named as Neighbourhood Zagreb index (M N) is presented. Here the chemical importance of this newly introduced index is studied and some explicit results for this index of different product graphs such as Cartesian, Tensor and Wreath product is derived. Some of these results are applied to obtain the Neighbourhood Zagreb index of several chemically important graphs and nano-structures.

Proyecciones (Antofagasta), 2020

Complex & Intelligent Systems, 2021

Topological index is a numerical value associated with a chemical constitution for correlation of... more Topological index is a numerical value associated with a chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this work, some new indices based on neighborhood degree sum of nodes are proposed. To make the computation of the novel indices convenient, an algorithm is designed. Quantitative structure property relationship (QSPR) study is a good statistical method for investigating drug activity or binding mode for different receptors. QSPR analysis of the newly introduced indices is studied here which reveals their predicting power. A comparative study of the novel indices with some well-known and mostly used indices in structure-property modelling and isomer discrimination is performed. Some mathematical properties of these indices are also discussed here.

Biointerface Research in Applied Chemistry, 2020

The neighborhood M-polynomial is effective in recovering neighborhood degree sum based topologica... more The neighborhood M-polynomial is effective in recovering neighborhood degree sum based topological indices that predict different physicochemical properties and biological activities of molecular structures. Topological indices can transform the information found in molecular graphs and networks into numerical characteristics and thus make a major contribution to the study of structure-property and structure-activity relationships. In this work, the neighborhood M-polynomial of the para-line graph of some convex polytopes is obtained. From the neighborhood M-polynomial, some neighborhood degree-based topological indices are recovered. Applications of the work are described. In addition, a quantitative and graphical comparison is made.

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY, 2015

A signed graph may be defined as an ordered pair (G, Ïƒ) where G= (V, E) is the graph and Ïƒ is a... more A signed graph may be defined as an ordered pair (G, Ïƒ) where G= (V, E) is the graph and Ïƒ is a function called signature or sign mapping from E to the sign group {+, -}. People or friends are considered as the vertices and the relationships between these friends are considered as the edges. '+' sign is assigned to the edge for good relationship and '-' sign for bad relationship between the friends. Two terms friendship matrix or â€œjudgement matrix and character point C.P are introduced in this paper. Using the concept of friendship matrix and C.P in various fields the characteristics or performances could be evaluated. In this paper different problems have been considered and analysed with the help of signed graph.

Malaya Journal of Matematik, 2019

A graphical invariant is a real number related to a graph which is fixed under the graph isomorph... more A graphical invariant is a real number related to a graph which is fixed under the graph isomorphism. In chemical graph theory, these invariants are also called topological indices and these are play a vital role to predict various chemical and physical properties of different molecular structures. In this work, we generalized multiplicative version Zagreb indices and compute it for probabilistic neural network. Also, we compute the general Zagreb index or (a, b)-Zagreb index for the same network and compute some other degree based topological indices for some particular values of a and b. Keywords Probabilistic neural network, Vertex degree based topological indices, The general Zagreb index, Multiplicative version of general Zagreb index.

Acta Chemica Iasi, 2019

In this paper, four novel topological indices named as neighbourhood version of forgotten topolog... more In this paper, four novel topological indices named as neighbourhood version of forgotten topological index (FN ), modified neighbourhood version of Forgotten topological index (FN * ), neighbourhood version of second Zagreb index (M2 * ) and neighbourhood version of hyper Zagreb index (HMN ) are introduced. Here the relatively study depends on the structure-property regression analysis is made to test and compute the chemical applicability of these indices for the prediction of physicochemical properties of octane isomers. Also it is shown that these newly presented indices have well degeneracy property in comparison with other degree based topological indices. Some mathematical properties of these indices are also discussed here.

Mathematics, 2019

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problem... more The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy ...

Journal of Taibah University for Science, 2018

There is a very wide application of mathematics in communication theory, signal processing and ne... more There is a very wide application of mathematics in communication theory, signal processing and networking. A network is formed by nodes communicating with each other. Graph theory plays a vital role in the area of networking research. A topological index is a numeric quantity obtained from a graph structure which is invariant under graph isomorphism. In this study, we obtained a generalized degree-based topological index, called (a, b)-Zagreb index of some derived networks such as Sierpinski network, butterfly network, Benes network and mesh-derived network and hence consider some particular cases.

SpringerPlus, 2016

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this... more 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.

International Journal of Computer Applications, 2015

The eccentric connectivity index of a graph is defined as the sum of the products of eccentricity... more The eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the degree of vertices over all vertices of the graph, and the modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighbouring vertices over all vertices of the graph. In this study, we find eccentric connectivity index and modified eccentric connectivity index and their respective polynomial versions of corona product of two graphs. Finally, we calculate the eccentric connectivity index and modified eccentric connectivity index of some important classes of chemically interesting molecular graphs by specializing the components of corona product of graphs.

Mathematics, 2015

The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by repl... more The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-structures.

International Journal of Advanced Computer Science and Applications, 2015

The employee-employer relationship is an intricate one. In an industry, the employers expect to a... more The employee-employer relationship is an intricate one. In an industry, the employers expect to achieve performances in quality and production in order to earn profit, on the other side employees need good pay and all possible allowances and best advantages than any other industry. Our main objective of this paper is to analyze the relationship between employee and employer in workplace and discussed how to maintain a strong employee and employer relationship which can produce the ultimate success of an organization using Induced Fuzzy bi-model called Induced Fuzzy Cognitive Relational Maps (IFCRMs). IFCRMs are a directed special fuzzy digraph modelling approach based on expert's opinion. This is a non statistical approach to study the problems with imprecise information.