S PETHANACHI SELVAM

@sfrcollege.edu.in

Associate Professor of Mathematics
The Standard Fireworks Rajaratnam College for Women, Sivakasi

S PETHANACHI SELVAM


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https://researchid.co/pethanachiselvams

EDUCATION

Doctorate in Mathematics in Semigraphs

RESEARCH INTERESTS

Graph Theory - Semigraphs, Labeling, Domination
5

Scopus Publications

26

Scholar Citations

3

Scholar h-index

Scopus Publications

  • Reduced Second Zagreb Index and Bounds of Some Graph Operations
    K. Rengalakshmi, S. Pethanachi Selvam
    Mathematics and Statistics, 2025
    To link mathematics with the vast field of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship) research, the idea of the concept of chemical graph theory is introduced. Topological indices refer to numerical values or descriptors that encode the structural properties of a molecular graph. There are numerous topological indices that have been created and applied as a tool in QSAR/QSPR research up to this point. Among those indices, the reduced second Zagreb index (<img src=image/13440163_01.gif>) has been established in recent times. Combining two graphs results in a new graph, like the lexicographic product of a cycle with n vertices with the path on two vertices results in a closed fence graph, and a path on n vertices with a path on two vertices results in a fence graph whose index can be easily computed by our obtained results. In this article, we compute the <img src=image/13440163_01.gif> index for the join product, lexicographic product, and tensor product of any two simply connected graphs in terms of the first and second Zagreb index and the cardinality of the graphs' vertex and edge sets that are being used. For this, we use the degree of a vertex in the newly created graph that comes from an operation, as well as the vertex and edge set cardinality of the graphs involved in the process. In terms of maximum and minimum degree, we additionally establish certain lower and upper bounds for the aforementioned products. We further state the necessary and sufficient condition to obtain equality for the bounds. Furthermore, we deduce bounds on <img src=image/13440163_01.gif> index for the earlier mentioned products of certain graphical structures, such as paths and cycles, and verify the index for a closed fence graph for application purposes. In this way, various operations can be performed to obtain different chemical structures that exist in our everyday lives. The structural and chemical characteristics of the obtained chemical structure attained by the graph invariant can be used in drug delivery, pharmaceutical research, and research purposes.
  • Reduced Second Zagreb Index and Bounds of Graph Products
    Iaeng International Journal of Applied Mathematics, 2025
  • Corporate domination number of the cartesian product of cycle and path
    S. Padmashini, S. Pethanachi Selvam
    Mathematics and Statistics, 2021
    Domination in graphs is to dominate the graph G by a set of vertices <img src=image/13421349_01.gif>, vertex set of G) when each vertex in G is either in D or adjoining to a vertex in D. D is called a perfect dominating set if for each vertex v is not in D, which is adjacent to exactly one vertex of D. We consider the subset C which consists of both vertices and edges. Let <img src=image/13421349_02.gif> denote the set of all vertices V and the edges E of the graph G. Then <img src=image/13421349_03.gif> is said to be a corporate dominating set if every vertex v not in <img src=image/13421349_04.gif> is adjacent to exactly one vertex of <img src=image/13421349_04.gif>, where the set P consists of all vertices in the vertex set of an edge induced sub graph <img src=image/13421349_05.gif>, (E<sub>1</sub> a subset of E) such that there should be maximum one vertex common to any two open neighborhood of different vertices in V(G[E<sub>1</sub>]) and Q, the set consists of all vertices in the vertex set V<sub>1</sub>, a subset of V such that there exists no vertex common to any two open neighborhood of different vertices in V<sub>1</sub>. The corporate domination number of G, denoted by <img src=image/13421349_06.gif>, is the minimum cardinality of elements in C. In this paper, we intend to determine the exact value of corporate domination number for the Cartesian product of the Cycle <img src=image/13421349_07.gif> and Path <img src=image/13421349_08.gif>.
  • Some New Results on Lucky Labeling
    J. Ashwini, S.Pethanachi Selvam, R.B. Gnanajothi
    Baghdad Science Journal, 2021
    Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph Kn, Complete bipartite graph Km,n and Complete tripartite graph Kl,m,n. It has also been studied how the lucky number changes while adding a graph G with Kn and deleting an edge e from Kn.
  • Edge complete (p,2) semigraphs
    Ars Combinatoria, 2007

RECENT SCHOLAR PUBLICATIONS

  • Reduced Second Zagreb Index and Bounds of Graph Products.
    K Rengalakshmi, SP Selvam
    IAENG International Journal of Applied Mathematics 55 (11) , 2025
    2025
    Citations: 1
  • Reduced Second Zagreb Index and Bounds of Some Graph Operations
    K Rengalakshmi, SP Selvam
    MATHEMATICS AND STATISTICS 13 (1), 41-47 , 2025
    2025
  • Some new results on lucky labeling
    J Ashwini, SP Selvam, RB Gnanajothi
    Baghdad Science Journal 20 (1), 50 , 2023
    2023
    Citations: 6
  • THE CORPORATE DOMINATION NUMBER OF THE CARTESIAN PRODUCT OF TWO CYCLES
    S PADMASHINI, SP SELVAM
    2022
  • Corporate Domination Number of the Cartesian Product of Cycle and Path
    S Padmashini, S Pethanachi Selvam
    Mathematics and Statistics 9 (1), 1-7 , 2021
    2021
    Citations: 5
  • ON CORPORATE DOMINATION IN GRAPHS
    S Padmashini, SP Selvam
    Advances in Mathematics: Scientific Journal 10 (4), 1959–1967 , 2021
    2021
    Citations: 2
  • Corporate Domination Number of the Cartesian Product of Cycle and Path, Mathematics and Statistics. 9 (1)(2021) 1-7
    S Padmashini, SP Selvam
    DOI: https://doi. org/10.13189/ms , 2021
    2021
    Citations: 2
  • Corporate Domination Number of the Cartesian Product of Two Paths
    S Padmashini, SP Selvam
    A Conference Proceedings of, 84 , 2021
    2021
  • AT MOST EDGE 3 - SUM CORDIAL LABELING FOR SOME GRAPHS
    S Pethanachi Selvam, S Padmashini
    International Journal of Research in Engineering and Applied Sciences … , 2016
    2016
  • At most edge 3-sum cordial labeling for some graphs the standard
    SP Selvam, S Padmashini
    International Journal of Research in Engineering and Applied Sciences 6 (7 … , 2016
    2016
  • Some Results on Detour Radial Graph
    T Ganeshwari, S Pethanachi Selvam
    International Journal of Research in Engineering and Applied Sciences 5 (12 … , 2015
    2015
    Citations: 2
  • Inverse Complementary Domination Graph
    S Pethanachi Selvam, S Padmashini
    International Journal of Mathematics Trends and Technology 25 (1), 5-7 , 2015
    2015
  • LINE CORPORATE DOMINATION GRAPH
    S PETHANACHI SELVAM, S PADMASHINI
    Mathematical Sciences International Research Journal 4 (2), 219-222 , 2015
    2015
  • SEMIGRAPHS IN I
    K Kayathri, SP Selvam
    ARS COMBINATORIA 123, 247-260 , 2015
    2015
  • k–SUM AND n–SUM CORDIAL LABELING OF SOME GRAPHS
    S Pethanachi Selvam, G Karthika
    IJMA 5 (10) , 2014
    2014
  • International Journal of Mathematical Archive-5 (5), 2014, 248-253 Available online through www. ijma. info ISSN 2229–5046
    SP Selvam, G Lathamaheswari
    2014
  • International Journal of Mathematical Archive-5 (10), 2014, 202-207 Available online through www. ijma. info ISSN 2229–5046
    SP Selvam, G Karthika
    International Journal of Mathematical Archive 5 (10) , 2014
    2014
  • Total 3-sum cordial labeling
    S Pethanachi Selvam, G Lathamaheswari
    IJMA 5 (5) , 2014
    2014
  • S and Lathamaheswari. G,“k–sum cordial labeling for some graphs”
    P Selvam
    IJMA 4 (3) , 2013
    2013
    Citations: 2
  • k sum cordial labelling for some graphs
    S Pethanachi Selvam, G Lathamaheswari
    International Journal of Mathematical Archive 4 (3), 253-259 , 2013
    2013

MOST CITED SCHOLAR PUBLICATIONS

  • Some new results on lucky labeling
    J Ashwini, SP Selvam, RB Gnanajothi
    Baghdad Science Journal 20 (1), 50 , 2023
    2023
    Citations: 6
  • Corporate Domination Number of the Cartesian Product of Cycle and Path
    S Padmashini, S Pethanachi Selvam
    Mathematics and Statistics 9 (1), 1-7 , 2021
    2021
    Citations: 5
  • Edge complete (p, 2) semigraphs
    K Kayathri, SP Selvam
    Ars Combinatoria 84, 65-76 , 2007
    2007
    Citations: 3
  • Edge complete (p, 3) semigraphs
    K Kayathri, SP Selvam
    ACTA CIENCIA INDICA MATHEMATICS 33 (2), 621 , 2007
    2007
    Citations: 3
  • ON CORPORATE DOMINATION IN GRAPHS
    S Padmashini, SP Selvam
    Advances in Mathematics: Scientific Journal 10 (4), 1959–1967 , 2021
    2021
    Citations: 2
  • Corporate Domination Number of the Cartesian Product of Cycle and Path, Mathematics and Statistics. 9 (1)(2021) 1-7
    S Padmashini, SP Selvam
    DOI: https://doi. org/10.13189/ms , 2021
    2021
    Citations: 2
  • Some Results on Detour Radial Graph
    T Ganeshwari, S Pethanachi Selvam
    International Journal of Research in Engineering and Applied Sciences 5 (12 … , 2015
    2015
    Citations: 2
  • S and Lathamaheswari. G,“k–sum cordial labeling for some graphs”
    P Selvam
    IJMA 4 (3) , 2013
    2013
    Citations: 2
  • Reduced Second Zagreb Index and Bounds of Graph Products.
    K Rengalakshmi, SP Selvam
    IAENG International Journal of Applied Mathematics 55 (11) , 2025
    2025
    Citations: 1
  • Reduced Second Zagreb Index and Bounds of Some Graph Operations
    K Rengalakshmi, SP Selvam
    MATHEMATICS AND STATISTICS 13 (1), 41-47 , 2025
    2025
  • THE CORPORATE DOMINATION NUMBER OF THE CARTESIAN PRODUCT OF TWO CYCLES
    S PADMASHINI, SP SELVAM
    2022
  • Corporate Domination Number of the Cartesian Product of Two Paths
    S Padmashini, SP Selvam
    A Conference Proceedings of, 84 , 2021
    2021
  • AT MOST EDGE 3 - SUM CORDIAL LABELING FOR SOME GRAPHS
    S Pethanachi Selvam, S Padmashini
    International Journal of Research in Engineering and Applied Sciences … , 2016
    2016
  • At most edge 3-sum cordial labeling for some graphs the standard
    SP Selvam, S Padmashini
    International Journal of Research in Engineering and Applied Sciences 6 (7 … , 2016
    2016
  • Inverse Complementary Domination Graph
    S Pethanachi Selvam, S Padmashini
    International Journal of Mathematics Trends and Technology 25 (1), 5-7 , 2015
    2015
  • LINE CORPORATE DOMINATION GRAPH
    S PETHANACHI SELVAM, S PADMASHINI
    Mathematical Sciences International Research Journal 4 (2), 219-222 , 2015
    2015
  • SEMIGRAPHS IN I
    K Kayathri, SP Selvam
    ARS COMBINATORIA 123, 247-260 , 2015
    2015
  • k–SUM AND n–SUM CORDIAL LABELING OF SOME GRAPHS
    S Pethanachi Selvam, G Karthika
    IJMA 5 (10) , 2014
    2014
  • International Journal of Mathematical Archive-5 (5), 2014, 248-253 Available online through www. ijma. info ISSN 2229–5046
    SP Selvam, G Lathamaheswari
    2014
  • International Journal of Mathematical Archive-5 (10), 2014, 202-207 Available online through www. ijma. info ISSN 2229–5046
    SP Selvam, G Karthika
    International Journal of Mathematical Archive 5 (10) , 2014
    2014