Article ID: MTJPAM-D-20-00056

Title: Zagreb Indices of Square Snake Graphs


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00056; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 165-171

Document Type: Research Paper

Author(s): Pushpalatha Mahalank a , Bhairaba Kumar Majhi b , Sadik Delen c , Ismail Naci Cangul d

aDepartment of Mathematics, SDM College of Engineering and Technology, Dharwad-580002, Karnataka, India

bDepartment of Mathematics, School of Applied Sciences, Centurion University of Technology and Management, Odisha, India

cBursa Uludag University, Department of Mathematics, Gorukle 16059 Bursa, Turkey

dBursa Uludag University, Department of Mathematics, Gorukle 16059 Bursa, Turkey

Received: 29 December 2020, Accepted: 11 February 2021, Published: 25 April 2021.

Corresponding Author: Ismail Naci Cangul (Email address: cangul@uludag.edu.tr)

Full Text: PDF

Abstract

Several lattice structures that can be thought as graphs are useful in the study of large networks. In this work, we study 15 topological graph indices from the class of Zagreb indices of some interesting lattice structures called snake graphs. We use vertex and edge partitions of these graphs and calculate their indices by means of these partitions.

Keywords: Graph, Zagreb index, Vertex degrees, Graph index, Square snake graphs

References:
  1. A. R. Bindusree, I. N. Cangul, V. Lokesha and A. S. Cevik, Zagreb polynomials of three graph operators, Filomat 30 (7), 1979-1986, 2016, DOI: 10.2298/FIL1607979B.
  2. J. P. Bradshaw, P. Lampe and D. Ziga, Snake graphs and their characteristic polynomials, arXiv:1910.11823v1.
  3. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces, J. Algebra 382, 240-281, 2013.
  4. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces II: Selfcrossing snake graphs, Math. Z. 281 (1), 55-102, 2015.
  5. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings, International Mathematics Research Notices rnx157, 2017.
  6. I. Canakci and R. Schiffler, Cluster algebras and continued fractions, Compos. Math. 154 (3), 565-593, 2018.
  7. K. Ch. Das, N. Akgunes, M. Togan, A. Yurttas, I. N. Cangul and A. S. Cevik, On the first Zagreb index and multiplicative Zagreb coindices of graphs, An. Şt. Univ. Ovidius Constanţa, 24 (1), 153-176, 2016.
  8. K. Ch. Das, M. Togan, A. Yurttas, A. S. Cevik and I. N. Cangul, The multiplicative Zagreb indices of graph operations, J. Inequal. Appl. 2013:90, 2013, DOI 10.1186/1029-242X-2013-90.
  9. B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (4), 1184-1190, 2015.
  10. I. I. Jadav and G. V. Ghodasara, Snakes related strongly*-graphs, International Journal of Advanced Engineering Research and Science 3 (9), 240-245, 2016.
  11. X. Li and J. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54, 195-208, 2005.
  12. V. Lokesha, S. B. Shetty, P. S. Ranjini and I. N. Cangul, Computing ABC, GA, Randic and Zagreb indices, Enlightments of Pure and Applied Mathematics 1 (1), 17-28, 2015.
  13. P. Mahalank, M. Demirci and I. N. Cangul, Third Zagreb index of graphs with added edges, Preprint.
  14. P. S. Ranjini, V. Lokesha and I. N. Cangul, On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput. 218, 699-702, 2011.
  15. P. S. Ranjini, M. A. Rajan and V. Lokesha, On Zagreb indices of the sub-division graphs, Int. J. of Math. Sci. & Eng. Appns. 4, 221-228, 2010.
  16. R. Shiffler, Snake graphs, perfect matchings and continued fractions, Snapshots of Modern Mathematics form Oberwolfach, 1, 2019, Mathematisches Forschungsinstitut Oberwolfach, DOI: 10.14760/SNAP-2019-001-EN
  17. M. Togan, A. Yurttas and I. N. Cangul, Some formulae and inequalities on several Zagreb indices of r-subdivision graphs, Enlightments of Pure and Applied Mathematics 1 (1), 29-45, 2015.
  18. M. Togan, A. Yurttas and I. N. Cangul, All versions of Zagreb indices and coindices of subdivision graphs of certain graph types, Adv. Stud. Contemp. Math. 26 (1), 227-236, 2016.
  19. M. Togan, A. Yurttas, A. S. Cevik and I. N. Cangul, Effect of edge deletion and addition on Zagreb indices of graphs. In: Tas, K., Baleanu, D., Machado, J. (eds), Mathematical Methods in Engineering, Theoretical Aspects, Nonlinear Systems and Complexity, Springer 23, 191-201, 2019.
  20. G. B. A Xavier, E. Suresh and I. Gutman, Counting relations for general Zagreb indices, Kragujevac J. Math. 38 (1), 95-103.
  21. A. Yurttas, M. Togan and I. N. Cangul, Zagreb indices of graphs with added edges, Proc. Jangjeon Math. Soc. 21 (3), 385-392, 2018.