On the extremal total reciprocal edge-eccentricity of trees

Abstract

The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and physical properties. If $G=(V_G,E_G)$ is a simple connected graph, then the total reciprocal edge-eccentricity (REE) of $G$ is defined as ${\xi }^{ee}(G)={\sum }_{uv\in E_G}(1/{\epsilon }_G(u)+1/{\epsilon }_G(v))$, where ${\epsilon }_G(v)$ is the eccentricity of the vertex $v$. In this paper we first introduced four edge-grafting transformations to study the mathematical properties of the reciprocal edge-eccentricity of $G$. Using these elegant mathematical properties, we characterize the extremal graphs among $n$-vertex trees with given graphic parameters, such as pendants, matching number, domination number, diameter, vertex bipartition, et al. Some sharp bounds on the reciprocal edge-eccentricity of trees are determined.

16pages, 8figures, Journal of Mathematics Analysis and Applications (2015)

References in corpus (2)

• Eccentric Connectivity Index of Chemical Trees
• The Connectivity and the Harary Index of a Graph

Cited by in corpus (1)

• On the maximum CEI of graphs with paprameters