Ordering Tricyclic Connected Graphs Having Minimum Degree Distance

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Abbottabad University of Science and Technology‎, ‎Abbottabad‎, ‎KPK‎, ‎Pakistan

10.22052/ijmc.2025.255360.1895

Abstract

‎Degree distance D'(G) is an important molecular descriptor which provides valuable insights into the connectivity and properties of molecular graphs‎, ‎making it a powerful tool in diverse areas of chemical graph theory‎. ‎This descriptor has attained much attention in the recent past for its broad range of applicability in different problems of chemical graph theory‎. ‎Ordering of graphs with certain parameters allows chemists to identify patterns and trends of different chemical compounds and as a result predict their reaction behavior accordingly‎. ‎In this paper‎, ‎the first sixteen tricyclic graphs are presented which have minimum degree distances (in ascending order) if $n\ge31$.

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References

[1] A. A. Dobrynin and A. A. Kochetova, Degree distance of a graph: a degree analog of the Wiener index, J. Chem. Inf. Comput. Sci. 34 (1994) 1082–1086, https://doi.org/10.1021/ci00021a008.
[2] I. Tomescu, Ordering connected graphs having small degree distances, Discrete Appl. Math. 158 (2010) 1714–1717, https://doi.org/10.1016/j.dam.2010.05.023.
[3] I. Tomescu and S. Kanwal, Ordering connected graphs having small degree distances. II, MATCH Commun. Math. Comput. Chem. 67 (2012) 425–437.
[4] I. Tomescu and S. Kanwal, Unicyclic connected graphs having smallest degree distances, Util. Math. 97 (2015) 161–181.
[5] M. Dragan and I. Tomescu, Bicyclic connected graphs having smallest degree distances, In 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) IEEE (2019) 105–108, https://doi.org/10.1109/SYNASC49474.2019.00023.
[6] W. Zhu, S. Hu and H. Ma, A note on tricyclic graphs with minimum degree distance, Discrete Math. Algorithms Appl. 3 (2011) 25–32, https://doi.org/10.1142/S1793830911000985.
Iranian Journal of Mathematical Chemistry
Volume 16, Issue 3
In Progress
September 2025
Pages 199-205

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