journal-of-information-and-optimization-sciences Journal of Information and Optimization Sciences 2169-0103 0252-2667 Taru Publications 10.47974/JIOS-2140 Topological indices of johnson graphs and their complements Dadhwal Madhu Department of Mathematics & Statistics, Summer Hill, Himachal Pradesh University, Shimla, Himachal Pradesh, 171005, India Pankaj Department of Mathematics, Government College Chamba, Chamba, Himachal Pradesh, 176314, India Ankita Department of Chemistry, Summer Hill, Himachal Pradesh University, Shimla, Himachal Pradesh, 171005, India 1 18 11 07 2026

The connectivity of the complements of the Johnson graphs π’₯(β„΅, 𝓇) is completely characterized for every β„΅ β‰₯ 2𝓇. A combinatorial identity as a variation of vandermonde’s identity has been established to compute the Wiener index of Johnson graphs π’₯(β„΅, 𝓇) and their compliments π’₯(β„΅, 𝓇) Β (whenever connected) by utilizing the vertex-transitivity of both the families of graphs. In addition, the Szeged index of π’₯(β„΅, 𝓇) and π’₯(β„΅, 𝓇) is also obtained by using the edge transitivity and examining a connection between the topology of the vertices in both the graphs, respectively, because the complement of a symmetric graph need not to be edge-transitive, in particular, π’₯(β„΅, 𝓇) is not edge transitive for 𝓇 β‰  1, 2 & β„΅-1.

 Johnson graph Wiener index Szeged index Complement Connectivity access open retracted no