S. Mukwembi

Lower Bounds on the Eccentric Connectivity Index in Terms of the Irregularity Index

Let G be a connected simple graph of order n≥3, and let ξc(G)=∑v∈V(G)ecG(v)degG(v) denote its eccentric connectivity index. We study the lower bounds for ξc(G) in terms of the irregularity index t(G), defined as the number of distinct vertex degrees of G. For t=t(G)≥2, we prove that ξc(G)≥3n+t2−3t−1, which reduces to t...