## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2017 (2017), Article ID 4180650, 8 pages.

### Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs

#### Abstract

The Gutman index of a connected graph $G$ is defined as $\mathrm{G}\mathrm{u}\mathrm{t}(G)={\sum}_{u\ne v}d(u)d(v)d(u,v)$, where $d(u)$ and $d(v)$ are the degree of the vertices $u$ and $v$ and $d(u,v)$ is the distance between vertices $u$ and $v$. The Detour Gutman index of a connected graph $G$ is defined as $\u200a\u200a\mathrm{G}\mathrm{u}\mathrm{t}\left(G\right)={\sum}_{u\ne v}d(u)d(v)D(u,v)$, where $D(u,v)$ is the longest distance between vertices $u$ and $v$. In this paper, the Gutman index and the Detour Gutman index of pseudo-regular graphs are determined.

#### Article information

**Source**

J. Appl. Math., Volume 2017 (2017), Article ID 4180650, 8 pages.

**Dates**

Received: 24 May 2017

Accepted: 27 June 2017

First available in Project Euclid: 19 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1505786436

**Digital Object Identifier**

doi:10.1155/2017/4180650

**Mathematical Reviews number (MathSciNet)**

MR3690380

#### Citation

Kavithaa, S.; Kaladevi, V. Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs. J. Appl. Math. 2017 (2017), Article ID 4180650, 8 pages. doi:10.1155/2017/4180650. https://projecteuclid.org/euclid.jam/1505786436