@article{Article_78,

title = {Terminal eccentricity indices of graphs},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2024},

issue = {1},

issn = { 2783-5456 },

year = {2023},

url = {http://cccs.sgh.ac.ir/Articles/2024/issue 1/1-6-Terminaleccentricityindicesofgraphs.pdf},

author = {Harishchandra S. Ramane and Deepa V. Kitturmath and and Kavita Bhajantri},

keywords = {Eccentricity of a vertex, Terminal eccenticity of a vertex, Terminal eccentricity indices.},

abstract = {Let $V_T(G)$ be the set of pendent vertices of $G$ and $d(u, v)$ be the distance between the vertices $u$ and $v$. The terminal eccentricity of a vertex $u$ is defined as $te_G(u)= \max \{d(u, v) \; | \; v \in V_T(G)\}$. In this paper we introduce new topological indices of graphs called as first and second terminal eccentricity indices and are defined as \[ TE_1(G) = \sum_{uv \in E(G)} [te_G(u)+te_G(v)] \;\;\; \text{and} \;\;\; TE_2(G) = \sum_{uv \in E(G)} te_G(u)te_G(v), \] where $E(G)$ is the edge set of $G$. We discuss properties of terminal eccentricity indices of graphs and carry regression analysis of these indices with the chemical properties of benzenoid hydrocarbons. The terminal eccentricity indices are useful in the graphs where pendent vertices exists.}

};