On Extremal General Multiplicative Zagreb Indices

نویسندگان

1 Department of Mathematics‎, ‎Wolkite University‎, ‎Ethiopia

2 Department of Mathematics‎, ‎Wolkite University‎, ‎Ethiopia

3 Department of Mathematics‎, ‎Wolkite University‎, ‎Ethiopia

doi
10.22052/ijmc.2025.255619.1918
چکیده

‎The first general multiplicative Zagreb index $P_1^a(G)$ is the product of the degree of each vertex $v$ in $G$‎, ‎raised to the power $a$ and the second general multiplicative Zagreb index $P_2^a(G)$ is the product of the degree of each vertex $v$ in $G$‎, ‎raised to the power $a$ times the degree of $v$‎, ‎where $a$ is a non-zero real number‎.‎In this study‎, ‎we present bounds on the general multiplicative Zagreb indices for trees and unicyclic graphs‎. ‎We also provide bounds for the first general multiplicative Zagreb index for trees‎.‎Additionally‎, ‎we identify all the extremal graphs for each bound mentioned as best as possible‎.

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