Inverse degree index of graphs with a given cyclomatic number-Reference-Cited by-同舟云学术

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Inverse degree index of graphs with a given cyclomatic number

Published:2023 Issue:27 Volume:37 Page:9371-9376
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Akbari Saieed¹,Doslic Tomislav²,Nahvi Nasim¹

Affiliation:

1. Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

2. University of Zagreb Faculty of Civil Engineering, Zagreb, Croatia + Faculty of Information Studies, Novo Mesto, Slovenia

Abstract

We investigate how the inverse degree index of graphs depends on their cyclomatic number. In particular, we provide sharp lower bounds on the inverse degree index over all graphs on a given number of vertices with a given cyclomatic number. We also deduce some structural properties of extremal graphs. Some open questions regarding the upper bound over the same class of graphs are discussed and some possible further developments are indicated.

Publisher

National Library of Serbia

Reference15 articles.

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2. L. E. Allem, R. O. Braga, A. Pastine, Randić index and energy, MATCH Commun. Math. Comput. Chem. 83 (2020), 611-622.

3. G. Arizmendi, O. Arizmendi, Energy of a graph and Randić index, Lin. Alg. Appl. 609 (2021), 332-338.

4. P. N. Balister, B. Bollobás, S. Gerke, The generalized Randić index of trees, J. Graph Theory 56 (2007), 270-286.

5. B. Bollobás, P. Erdõs, A. Sarkar, Extremal graphs for weights, Discrete Math. 200 (1999), 5-19.

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