D-Index of Certain Ladder Graphs

Authors

  • Gashaw Aziz Mohammed Saleh Depaermnt of Mathematics, College of Science, Salahaddin University-Erbil, Erbil, Kurdistan Region, IRAQ.

DOI:

https://doi.org/10.29304/jqcsm.2024.16.31668

Keywords:

D-distance, Wiener D-index, Ladder graph, Semi-ladder graph

Abstract

For any two distinct vertices ,  of a connected graph , the -distance  , in which the minimum is taken over all  paths, and  is the length of the path . The -index of  is defined as . In this paper, we obtained a formula for -index  or Wiener -index  , where  is the ladder graph, . Also, we obtained the Wiener -index and Wiener index of semi-Ladder graph .

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References

H. J. Ahmed, A. M. Ali and G. A. MohammedSaleh, “Detour polynomials of some cog-special graphs”, Journal of Information & Optimization Sciences, Vol.2, No.43 (2022), pp.261-278, DOI: 10.1080/02522667.2021.1984562.

A. M. Ali and A. S. Aziz, “A relation between D-index and Wiener index for r-regular graphs”, International J. of Maths. And Math. Scs., Vol.2020(2020), 6 pages.

A. A. Ali and G. A. MohammedSaleh, “The detour polynomial of Ladder graphs”, Raf. J. Comp. Sci. and Maths, Vol.9, No.1(2012), pp.139-146.

A. A. Ali and W. A. Saeed, “Wiener polynomials of Steiner distance of graphs”, Journal of Applied Sciences, Vol.8, No.2 (2006), pp.64-71.

D. R. Babu and P. L. N. Varma, “D-distance in graphs”, Golden Research Thoughts, Vol.9, No.2 (2013), pp.1-6, DOI: 10.9780/2231-5063/292013/1696.

F. Buckley and F. Harary, “Distance in Graphs”, Addison-Wisely Publishing Company, (1990).

G. Chartrand, E. Escuardro and P. Zhang, “Detour distance in graphs”, J. Combin. Comput., Vol.53(2005), pp.75-94.

G. Chartrand; L. Lesniak and P. Zhang “Graphs & Digraphs, 6 Edition”, Chapman and Hall/CRC, (2015).

D. F. Hsu, “On container width and length in graphs, groups and networks, IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, Vol.E77-A, No. 4 (1994), pp.668-680.

J. K. Kathiresan and G. Marimuthu, “Superior distance in graphs”, J. Combin. Comput., Vol.61 (2007), pp.73-80.

G. A. MohammedSaleh, “The Restricted Detour Radial Graphs”, Palestine Journal of Mathematics, Vol.I, No.12 (2023), pp.146-154.

G. A. MuhammedSaleh and P. H. Aziz, “Computation of Detour D-Index and Average Detour D-Distance of Specific Graphs”, Passer, Vol.6, No.1 (2024), pp. 230-236.

V. V. Rao and P. L. N. Varma, “Detour distance in graphs w.r.t. D-distance”, International Journal of Sciences and Research, Vol.7, No.73 (2017), pp.19-28.

B. E. Sagan, Y. N. Yeh and P. Zhang, “The Wiener polynomial of a graph”, International J. of Quantum Chemistry, Vol.60,No.5 (1990), pp.959-969.

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Published

2024-09-30

How to Cite

Aziz Mohammed Saleh, G. (2024). D-Index of Certain Ladder Graphs. Journal of Al-Qadisiyah for Computer Science and Mathematics, 16(3), Math. 71–80. https://doi.org/10.29304/jqcsm.2024.16.31668

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Section

Math Articles