Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

Resolving Topological Indices of Graphs

Document Type : Research Paper

Authors
Badekara Sooryanarayana 1
Sogenahalli Boraiah Chandrakala 2
Gujar Ravichandra Roshini 3
Mallappa Vishu Kumar 4
1 Department of Mathematics, Dr. Ambedkar Institute of Technology, Bengaluru, Pin 560 056, India
2 Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, Pin 560 064, India
3 Department of Mathematics, Nagarjuna College of Engineering and Technology, Bengaluru, Pin 562110, India
4 Department of Mathematics, Reva University, Bengaluru, Pin 560 064, India
10.22052/ijmc.2022.242888.1567
Abstract
Topological indices are graph invariants most suitable for underlined structures of chemical compounds. Most of the topological indices are defined on the well-known graph concepts such as degree of a vertex, distances, eccentricity of a vertex etc. In this paper, new type of degree of a vertex is defined with the aid of resolving property of the graph as the minimum cardinality of a resolving set containing that vertex. The mathematical properties of this newly defined degree is established with the help of standard graphs and an attempt to analyze its applicability in chemical compounds are carried by taking silicate structures.
Keywords
Resolving set
Topological index
Zagreb index
Subjects
  1. G. Chartrand, L. Eroh, M. A. Johnson and O. R. Oellermann, Resolvability in graphs and metric dimension of a graph, Discrete Appl. Math. 105 (1-3) (2000) 99-113.
  2. G. Chartrand and P. Zhang, A First Course in Graph Theory, Western Michigan University. Dover Publications, INC. Mineola, New York, 2012.
  3. I. Gutman and N. Trinajstić, Graph theory and molecular orbitals III. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.
  4. F. Harary and R. A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976) 191–195.
  5. A. M. Hanan Ahmed, A. Alwardi and M. Ruby Salestina, On domination topological indices of graphs, Int. J. Anal. Appl. 19 (1) (2021) 47–64.
  6. S. Khuller, B. Raghavachari and A. Rosenfeld, Land marks in graphs, Discrete Appl. Math. 70 (3) (1996) 217–229.
  7. K. Mitr, S. P. D’Silva and B. Sooryanarayana, Zagreb alliance indices, Adv. Math. Sci. J. 10 (3) (2021) 1273–1284.
  8. M. Naeem, M. K. Siddiqui, Sh. Qaisar, M. Imran and M. R. Farahani, Computing topological indices of 2-dimensional silicon-carbons, U.P.B. Sci. Bull., Series B 80 (4) (2018) 115-135.
  9. Nadeem, S. Ahmad, M. K. Siddiqui and M. Naeem, Topological descriptor of 2-dimensional silicon carbons and their applications, Open Chem. 17 (1) (2019) 1473–1482.
  10. R. F. Bailey, J. Cáceres, D. Garijo, A. González, A. Márquezc, K. Meagherd and M. Luz Puertas, Resolving sets for Johnson and Kneser graphs, European J. Combin. 34 (4) (2013) 736–751.
  11. S. M. Kang, M. K. Siddiqui, N. A. Rehman, M. Naeem and M. H. Muhammad, Topological properties of 2-dimensional silicon-carbons, IEEE Access 8 (2018) 59362–59373.
  12. P. J. Slater, Leaves of trees, Congr. Numer. 14 (1975) 549–559.
  13. B. Sooryanarayana, K. Shreedhar and N. S. Narahari, Metric dimension of generalized wheels, Arab J. Math. Sci. 25 (2) (2019) 131–144.
  14. B. Sooryanarayana, A. S. Suma and S. B. Chandrakala, Certain varieties of resolving sets of a graph, J. Indones. Math. Soc. 27 (1) (2021) 103–114.
Iranian Journal of Mathematical Chemistry
Volume 13, Issue 3
Summer 2022
Pages 201-226