Original Research Article

Article volume = 2024 and issue = 1

Pages: 29–36

Article publication Date: December 05, 2023

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# Terminal eccentricity indices of graphs

#### Harishchandra S. Ramane(a), Deepa V. Kitturmath(b), and Kavita Bhajantri(c)

(a) Department of Mathematics, Karnatak University, Pavate Nagar, Dharwad - 580003, India.

(b) Department of Mathematics, KLE Technological University, Vidyanagar, Hubballi - 580031, India.

(c) Department of Mathematics, JSS Banashankari Arts, Commerce and S.K. Gubbi Science College, Dharwad - 580004, India.

##### 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.

##### Keywords:

Eccentricity of a vertex, Terminal eccenticity of a vertex, Terminal eccentricity indices.

##### References:

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##### Cite this article as:

- Harishchandra S. Ramane, Deepa V. Kitturmath, and Kavita Bhajantri, Terminal eccentricity indices of graphs, Communications in Combinatorics, Cryptography & Computer Science, 2024(1), PP.29–36, 2023
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