Transit in corona product of graphs

Authors

DOI:

https://doi.org/10.23755/rm.v47i0.860

Keywords:

Geodesic, Transit Index, Transit Identical, Corona product

Abstract

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 of vertices in Corona product of graphs. An expression for transit of vertices in $G_1\circ G_2$, where $G_1$ and $G_2$ are arbitrary is derived. We also compute transit for vertices in $G_1\circ G_2$, in the case where $G_1$ is a path, a cycle, a star, a complete graph and a complete bipartite graph.

Author Biographies

  • Reshmi KM, Govt. Arts and Science College, Kozhikode, Kerala-673018
    Assistant Professor, Department of Mathematics
  • Raji Pilakkat, University of Calicut, Malappuram, India-673365
    Professor, Department of Mathematics

References

V. Agnes, "Degree distance and gutman index of corona product of graphs," Transactions on Combinatorics, vol. 4, 2015.

J. Bondy and U. Murty, "Graph Theory," Springer, 2019.

R. Frucht and F. Harary, "On the corona of two graphs," Aeq. Math., vol. 4, pp. 322-325, 1970. doi: https://doi.org/10.1007/BF01844162.

P.S. Gajendra, A. Borah, and S. Ray, "A review paper on corona product of graphs," Advances and Applications in Mathematical Sciences, vol. 19, pp. 1047-1054, 2020.

H. Harary, "Graph Theory," Addison Wesley, 1969.

K.M. Reshmi and Pilakkat Raji, "Transit index of a graph and its correlation with mon of octane isomers," Advances in Mathematics: Scientific Journal, vol. 9, 2020. doi: https://doi.org/10.37418/amsj.9.4.39.

Shimbel and Alfonso, "Structural parameters of communication networks," Bulletin of Mathematical Biophysics, vol. 15, pp. 501-507.

Wagner.S and Wang.H, "Introduction to chemical graph theory," Taylor and Francis Group, Boca Raton, FL: CRC Press, 2019.

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Published

2023-06-30

Issue

Vol. 47 (2023)

Section

Volume 47-2023

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