Transit Index of Subdivision Graphs

K. M. Reshmi; Raji Pilakkat

doi:10.26713/cma.v12i3.1565

Authors

K. M. Reshmi Department of Mathematics, Government Engineering College, Kozhikode
Raji Pilakkat Department of Mathematics, University of Calicut, Malappuram

DOI:

https://doi.org/10.26713/cma.v12i3.1565

Keywords:

Transit index, Majorized shortest path, Transit decomposition, Subdivision graph

Abstract

The concept of transit of a vertex and transit index of a graph was defined by the authors in their previous work. The transit of a vertex v is "the sum of the lengths of all shortest path with v as an internal vertex” and the transit index of a graph \(G\) is the sum of the transit of all the vertices of it. In this paper, we investigate transit index of sub-division graphs.

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References

G. Harary, Graph Theory, Addison Wesley, Reading, Massachusetts (1969).

M. Eliasi, G. Raeisi and B. Taeri, Wiener index of some graph operations, Discrete Applied Mathematics 160 (9), 1333 – 1344, DOI: 10.1016/j.dam.2012.01.014.

O. Melnikov, V. Sarvanov, R. Tyshkevich, V. Yemelichev and I. Zverovich, Exercises in Graph Theory, Springer, Dordrecht (1998), DOI: 10.1007/978-94-017-1514-0.

P. S. Ranjini and V. Lokesha, Eccentric connectivity index, hyper and reverse-Wiener indices of the subdivision graph, General Mathematics Notes 2(2) (2011), 34 – 46.

K. M. Reshmi and R. Pilakkat, Transit index of a graph and its correlation with MON of octane isomers, Advances in Mathematics: Scientific Journal 9(4) (2020), 1825 – 1833, DOI: 10.37418/amsj.9.4.39.

K. M. Reshmi and R. Pilakkat, Transit index of various graph classes, Malaya Journal of Matematik 8(2) (2020), 494 – 498, DOI: 10.26637/MJM0802/0029.

R. Amin and S. M. A. Nayeem, On the F-index and F-coindex of the line graphs of the subdivision graphs, Malaya Journal of Matematik 6(2) (2018), 362 – 368, DOI: 10.26637/MJM0602/0010.

S. Imran, M. K. Siddiqui, M. Imran and M. F. Nadeem, Computing topological indices and polynomials for line graphs, Mathematics 6 (2018), 137, DOI: 10.3390/math6080137.

S. Wagner and H. Wang, Introduction to Chemical Graph Theory, CRC Press, Taylor & Francis Group, Boca Raton, FL (2019), DOI: 10.1201/9780429450532.