## Journal of Applied Mathematics

### 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 $\mathrm{G}\mathrm{u}\mathrm{t}(G)={\sum }_{u\ne v}d(u)d(v)D(u,v)$, 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
Accepted: 27 June 2017
First available in Project Euclid: 19 September 2017

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

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