On Connected Graphs Having the Maximum Connective Eccentricity Index

Abstract

The connective eccentricity index (CEI) of a connected graph G is defined as $$\xi ^{ee}(G)=\sum _{u\in V_G}[d_G(u)/\varepsilon _G(u)]$$ , where $$d_G(u)$$ and $$\varepsilon _G(u)$$ are the degree and eccentricity, respectively, of the vertex $$u\in V_G$$ of G. In this paper, graphs with the maximum CEI are characterized from the class of all connected graphs of a fixed order and size. Graphs having maximum CEI are also determined from some other well-known classes of connected graphs of a given order; namely, the Halin graphs, triangle-free graphs, planar graphs and outer-planar graphs.