On the first general Zagreb eccentricity index

Muhammad Kamran Jamil; Muhammad Imran; Aisha Javed; Roslan Hasni; Muhammad Kamran Jamil; Muhammad Imran; Aisha Javed; Roslan Hasni

doi:10.3934/math.2021032

AIMS Mathematics

2021, Volume 6, Issue 1: 532-542. doi: 10.3934/math.2021032

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Research article

On the first general Zagreb eccentricity index

1.
Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan
2.
Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, United Arab Emirates
3.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan
4.
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

Received: 19 August 2020 Accepted: 09 October 2020 Published: 20 October 2020
MSC : 05C09, 05C92

In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.
- eccentricity of vertices,
- first general Zagreb eccentricity index,
- extremal graphs
Citation: Muhammad Kamran Jamil, Muhammad Imran, Aisha Javed, Roslan Hasni. On the first general Zagreb eccentricity index[J]. AIMS Mathematics, 2021, 6(1): 532-542. doi: 10.3934/math.2021032

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Abstract

In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.

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