Super Edge-Connectivity and Zeroth-Order Randić Index

Abstract

Define the zeroth-order Randić index as R0(G)=∑x∈V(G)1dG(x),{R^0}\left( G \right) = \sum\nolimits_{x \in V\left( G \right)} {{1 \over {\sqrt {{d_G}} \left( x \right)}},} where dG(x) denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs, respectively, to be super edge-connected in terms of the zeroth-order Randić index.

Keywords

• zeroth-order randić index
• super edge-connected
• degree
• triangle-free graph
• minimum degree
• 05c20