On Edge Mostar Index of Graphs

Document Type : Research Paper

Authors

1 College of Mathematics and Statistics Hunan Normal University

2 School of Mathematics and Statistics, Hunan Normal University

Abstract

The edge Mostar index π‘€π‘œπ‘’(𝐺) of a connected graph 𝐺 is defined as π‘€π‘œπ‘’(𝐺)=Σ𝑒=𝑒𝑣∈𝐸(𝐺) |π‘šπ‘’(𝑒|𝐺)−π‘šπ‘£(𝑒|𝐺)|, where π‘šπ‘’(𝑒|𝐺)and π‘šπ‘£(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑒 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑒. In this paper, we determine the extremal values of edge Mostar index of some graphs. We characterize extremal trees, unicyclic graphs and determine the extremal graphs with maximum and second maximum edge Mostar index among cacti with size π‘š and 𝑑 cycles. At last, we give some open problems.

Keywords

Main Subjects

References

  1. M. Arockiaraj, J. Clement and N. Tratnik, Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems, Int. J. Quantum Chem. 119 (2019) e26043.
  2. T. DošliΔ‡, I. Martinjak, R. Škrekovski, S. TipuriΔ‡ SpuΕΎeviΔ‡ and I. Zubac, Mostar index, J. Math. Chem. 56 (2018) 2995-3013.
  3. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27 (1994) 9-15.
  4. I. Gutman and A. R. Ashrafi, The edge version of the Szeged index, Croat. Chem. Acta 81 (2008) 263-266.
  5. F. Hayat and B. Zhou, On cacti with large Mostar index, Filomat 33 (2019) 4865-4873.
  6. A. Tepeh, Extremal bicyclic graphs with respect to Mostar index, Appl. Math. Com put. 355 (2019) 319-324.
  7. N. Tratnik, Computing the Mostar index in networks with applications to molecular graphs, arXiv:1904.04131.
  8. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. 69 (1947) 17-20.
Iranian Journal of Mathematical Chemistry
Volume 11, Issue 2
July 2020
Pages 95-106

Files

Share

How to cite

Statistics