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

Harishchandra S. Ramane; Daneshwari D. Patil

doi:10.5644/SJM.21.01.03

Authors

Harishchandra S. Ramane Department of Mathematics, Karnatak University, Dharwad-580003, India
Daneshwari D. Patil Department of Mathematics, Sha. Sogamal Peeraju Oswal Government First Grade College, Muddebihal-586212, India

DOI:

https://doi.org/10.5644/SJM.21.01.03

Keywords:

Join of two graphs, Indu-Bala product, $\mathcal{CD}$-spectrum, $\mathcal{RCD}$-spectrum

Abstract

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.

Statistics

Abstract: 206 / PDF: 77

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