arXiv subjects

Anita Pal

Publications and source records attributed to Anita Pal.

12 recordsLinked to original sources

arXiv2019

QSPR analysis of some novel neighborhood degree based topological descriptors

Topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this work, some new indices based on neighbourhood degree sum of nodes are proposed. To make the computation of the novel indices convenient, an algorithm is designed. QSPR analysis of these newly introduced indices are studied here which reveals their predicting power. Some mathematical properties of these indices are also discussed here.

cs.DM↗

arXiv2019

On some new neighbourhood degree based indices

In this paper, four novel topological indices named as neighbourhood version of forgotten topological index (F_N), modified neighbourhood version of Forgotten topological index ($F_N^*$), neighbourhood version of second Zagreb index ($M_2^*$)and neighbourhood version of hyper Zagreb index ($HM_N$) 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.

physics.chem-ph↗

arXiv2019

The general Zagreb index of lattice networks

A topological index is a real number which is derived from a network or a graph by mathematically that characterizes the whole of its structural properties. Recently, there are various topological indices that have been introduced in mathematical chemistry to predict the properties of molecular topology. Among, the degree based topological indices such as Zagreb indices, forgotten topological index, redefined Zagreb index, Randic index, general first Zagreb index, symmetric division deg index and hence so forth are most important, because of their chemical significance. In this work, we study the general Zagreb index of hexagonal and triangular lattice networks.

math.CO↗

arXiv2018

On Neighbourhood Zagreb index of product graphs

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.

math.CO↗

arXiv2017

F-index of graphs based on new operations related to the join of graphs

The forgotten topological index or F-index of a graph is defined as the sum of degree cube of all the vertices of the graph. This index was introduced by Gutman and Trinajestić more than 40 years ago. In this paper, we derive F-index of new operations of subdivision graphs related to the graphs join.

math.CO↗

arXiv2017

Online Participatory Sensing in Double Auction Environment with Location Information

As mobile devices have been ubiquitous, participatory sensing emerges as a powerful tool to solve many contemporary real life problems. Here, we contemplate the participatory sensing in online double auction environment by considering the location information of the participating agents. In this paper, we propose a truthful mechanism in this setting and the mechanism also satisfies the other economic properties such as budget balance and individual rationality.

cs.GT↗

arXiv2016

Quality adaptive online double auction in participatory sensing

Agents (specially humans) with smart devices are stemming with astounding rapidity and that may play a big role in information and communication technology apart from being used only as a mere calling devices. Inculcating the power of smart devices carried by the agents in several different applications is commonly termed as participatory sensing (PS). In this paper, for the first time a truthful quality adaptive participatory sensing is presented in an online double auction environment. The proposed algorithm is simulated with a benchmark mechanism that adapts the existing McAfee's Double Auction (MDA) directly in the online environment.

cs.GT↗

arXiv2015

F-Index of Some Graph Operations

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total $π$-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53(4)(2015) 1184--1190.] reinvestigated the index and named it "forgotten topological index" or "F-index". In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nano-structures.

math.CO↗

arXiv2014

L(2,1)-labelling of Circular-arc Graph

An L(2,1)-labelling of a graph $G=(V, E)$ is $λ_{2,1}(G)$ a function $f$ from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The L(2,1)-labelling number denoted by $λ_{2,1}(G)$ of $G$ is the minimum range of labels over all such labelling. In this article, it is shown that, for a circular-arc graph $G$, the upper bound of $λ_{2,1}(G)$ is $Δ+3ω$, where $Δ$ and $ω$ represents the maximum degree of the vertices and size of maximum clique respectively.

cs.DM↗

arXiv2014

Connective eccentric index of 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.

math.CO↗

arXiv2014

Scheduling algorithm to select $k$ optimal programme slots in television channels: A graph theoretic approach

In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration of two {programme slots} have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. A set of programmes that are mutually exclusive in respect of time scheduling is called a session. We assume that a company sets the objective of selecting the popular programmes in $k$ parallel sessions among different channels so as to make its commercial advertisement reach the maximum number of viewers, that is, a company selects $k$ suitable programme slots simultaneously for advertisement. The aim of the paper is, therefore, to {help} the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme in $k$ parallel slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight $k$-colouring problem on an interval {graph}. An algorithm is designed to solve this just-in-time optimization problem using $O(kMn^2)$ time, where $n$ and $M$ represent the total number of programmes of all channels and the upper bound of the viewers of all programmes of all channels respectively. The problem considered in this paper is a daily life problem which is modeled by $k$-colouring problem on interval graph.

cs.DM↗

arXiv2014

Bounds for the modified eccentric connectivity index

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. This is a generalization of eccentric connectivity index. In this paper, we derive some upper and lower bounds for the modified eccentric connectivity index in terms of some graph parameters such as number of vertices, number of edges, radius, minimum degree, maximum degree, total eccentricity, the first and second Zagreb indices, Weiner index etc.

math.CO↗