Süleyman Ediz and Mesut Semiz

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 4, Pages 144—148

DOI: 10.7546/nntdm.2018.24.4.144-148

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## Details

### Authors and affiliations

Süleyman Ediz

*Faculty of Education, Yüzüncü Yıl University
Van, Turkey*

Mesut Semiz

*Faculty of Education, Yüzüncü Yıl University
Van, Turkey*

### Abstract

The reverse vertex degree of a vertex *v* of a simple connected graph *G* defined as *c _{v}* = Δ −

*d*+ 1, where Δ denotes the largest of all degrees of vertices of

_{v}*G*and

*d*denotes the number of edges incident to

_{v}*v*. The first reverse Zagreb beta index of a simple connected graph

*G*defined as

*CM*

^{β}_{1}(

*G*) = Σ

_{uv∈E(G)}(

*c*+

_{u}*c*). In this paper, we characterized maximum chemical trees with respect to the first reverse Zagreb beta index.

_{v}### Keywords

- Zagreb indices
- Reverse Zagreb indices

### 2010 Mathematics Subject Classification

- 05C07

### References

- Das, K. C., & Gutman, I. (2004) Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., 52, 103–112.
- Ediz, S. (2015) Maximum chemical trees of the second reverse Zagreb index, Pacific Journal of Applied Mathematics, 7, 291–295.
- Ediz, S. (2017) Extremal Chemical Trees of the First Reverse Zagreb Alpha Index, Mathematics Letters, 3, 46–49.
- Ediz, S. (2018) Maximal graphs of the first reverse Zagreb beta index, TWMS J. of Apl. Eng. Math., 8, 306–310.
- Ediz, S., & Cancan, M. (2016) Reverse Zagreb indices of Cartesian product of graphs, International Journal of Mathematics and Computer Science, 11, 51–58.
- Gutman, I., & Das, K. C. (2004) The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50, 83–92.
- Gutman, I., Ruščić, B., Trinajstić, N. , & Wilcox, C. F. (1975) Graph theory and molecular orbitals, XII. Acyclic polyenes, J. Chem. Phys., 62, 3399–3405.
- Gutman, I., & Trinajstić, N. (1971) Graph theory and molecular orbitals. Total
*π*-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535–538. - Nikolić, S., Kovačević, G., Miličević, A., & Trinajstić, N. (2003) The Zagreb indices 30 years after, Croat. Chem. Acta, 76, 113–124.
- Stevanović, S. (2011) On the relation between the Zagreb indices, Croat. Chem. Acta, 84, 17–19.
- Wiener, H. (1947) Structural determination of parafin boiling points, J. Am. Chem. Soc., 69, 17–20.

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## Cite this paper

Ediz, S., & Semiz, M. (2018). Extremal chemical trees of the first reverse Zagreb beta index. *Notes on Number Theory and Discrete Mathematics*, 24(4), 144-148, doi: 10.7546/nntdm.2018.24.4.144-148.