Degree sum (1/3)rd index of certain graphs

R. Rashmi; K. N.  Prakasha; Arun C.  Dixit; Ismail Naci  Cangul

doi:10.5269/bspm.78689

R. Rashmi Department of Mathematics, CIT Gubbi
K. N. Prakasha Vidyavardhaka College of Engineering
Arun C. Dixit Vidyavardhaka College of Engineering
Ismail Naci Cangul Bursa Uludag University

Abstract

In this paper, we have computed the degree sum $(1/3)^{rd}$ index of some double graphs, subdivision graphs and complement of standard graphs.Topological indices are numerical quantities linked to a graph structure which are frequently employed in computer science, mathematical biology, and theoretical chemistry. Degree based topological indices, such as degree sum $(1/3)^{rd}$ index offer important insights into the stability, reactivity, and branching of molecules. These indices are widely used to predict the physical, chemical, and biological characteristics of chemical compounds in the research of structure–property and structure–activity relationships (QSAR/QSPR). They are also helpful in network analysis, drug design, and nanostructure characterization.

Downloads

Download data is not yet available.

References

Das, K. C., Akgunes, N., Togan, M., Yurttas, A., Cangul, I. N., and Cevik, A. S. (2016). On the first Zagreb index and multiplicative Zagreb coindices of graphs. Analele Stiintifice ale Universitatii Ovidius Constanta, 24(1), 153–176.

Hosamani, S. M., Lokesha, V., Cangul, I. N., and Devendraiah, K. M. (2016). On certain topological indices of the derived graphs of subdivision graphs.

Lokesha, V., Shetty, S. B., Ranjini, P. S., and Cangul, I. N. (2015). Computing ABC, GA, Randic and Zagreb indices. Enlightenments of Pure and Applied Mathematics (EPAM), 1(1), 17–28.

Ranjini, P. S., Lokesha, V., and Cangul, I. N. (2011). On the Zagreb indices of the line graphs of the subdivision graphs. Applied Mathematics and Computation, 218, 699–702.

Prakasha, K. N., Kiran, K., and Rakshith, S. (2019). Randi´c Type SDI Index of Certain Graphs. TWMS Journal of Applied and Engineering Mathematics, 9(4), 894–900.

Ranjini, P. S., Rajan, M. A., and Lokesha, V. (2010). On Zagreb Indices of the Subdivision Graphs. International Journal of Mathematical Sciences & Engineering Applications (IJMSEA), 4, 221–228.

E. Sampathkumar, L. Pushpalatha, C. V. Venkatachalam and Pradeep Bhat, Generalized complements of a graph, Indian J. Pure Appl. Math, 29(6) (1998), 625-639.

Togan, M., Yurttas, A., Cangul, I. N., and Cevik, A. S. Zagreb indices and multiplicative Zagreb indices of double graphs of subdivision graphs. Preprint.

Togan, M., Yurttas, A., and Cangul, I. N. Zagreb and multiplicative Zagreb indices of r-subdivision graphs of double graphs. Preprint.

Togan, M., Yurttas, A., and Cangul, I. N. (2015). Some formulae and inequalities on several Zagreb indices of rsubdivision graphs. Enlightenments of Pure and Applied Mathematics (EPAM), 1(1), 29–45.

Togan, M., Yurttas, A., and Cangul, I. N. (2016). All versions of Zagreb indices and coindices of subdivision graphs of certain graph types. Advanced Studies in Contemporary Mathematics, 26(1), 227–236.

Vukicevic, D., Gutman, I., Furtula, B., Andova, V., and Dimitrov, D. (2011). Some observations on comparing Zagreb indices. MATCH Communications in Mathematical and in Computer Chemistry, 66, 627–645.

Yurttas, A., Togan, M., and Cangul, I. N. (2016). Zagreb indices and multiplicative Zagreb indices of subdivision graphs of double graphs. Advanced Studies in Contemporary Mathematics, 26(3), 407–416.