TY - JOUR
T1 - On the first general Zagreb eccentricity index
AU - Jamil, Muhammad Kamran
AU - Imran, Muhammad
AU - Javed, Aisha
AU - Hasni, Roslan
N1 - Publisher Copyright:
© 2021 the Author(s), licensee AIMS Press.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Eccentricity of vertices
KW - Extremal graphs
KW - First general Zagreb eccentricity index
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U2 - 10.3934/math.2021032
DO - 10.3934/math.2021032
M3 - Article
AN - SCOPUS:85094134715
SN - 2473-6988
VL - 6
SP - 532
EP - 542
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 1
ER -