Complementary Distance and Reciprocal Complementary Distance Spectrum for Indu-Bala Product of Graphs

For two graphs $G_1$ and $G_2$, graph obtained with two disjoint copies of join structure $G_1 \vee G_2$ by joining the corresponding vertices in $G_2$'s, is the Indu--Bala product $G_1 \blacktriangledown G_2$. Present work focuses on the study of complementary distance ($\mathcal{CD}$) and reciprocal complementary distance ($\mathcal{RCD}$) spectrum for Indu--Bala product of regular graphs via the concept of equitable partition. Hence note $\mathcal{CD}$ and $\mathcal{RCD}$ spectrum of dumbbell graph as a particular case of the Indu--Bala product.