This analysis reveals the complementary and reciprocal complementary distance spectra in regular graphs, suggesting potential applications in graph theory.
For two graphs G₁ and G₂, graph obtained with two disjoint copies of join structure G₁ G₂ by joining the corresponding vertices in G₂'s, is the Indu--Bala product G₁ G₂. Present work focuses on the study of complementary distance (CD) and reciprocal complementary distance (RCD) spectrum for Indu--Bala product of regular graphs via the concept of equitable partition. Hence note CD and RCD spectrum of dumbbell graph as a particular case of the Indu--Bala product.
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Ramane et al. (2025) studied this question.
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