On Zagreb Indices of Honeycomb Networks

The First and Second Zagreb Indices in Graph Theory: The first and second Zagreb indices are important degree-based topological indices used in graph theory. They are defined as follows: First Zagreb Index (M1): <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>G</mi> <mo>)</mo> <mo>=</mo> <munder> <mo>&sum;</mo> <mrow> <mi>u</mi> <mi>v</mi> <mo>&#x2208;</mo> <mi>E</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </munder> <mo>(</mo> <msub> <mi>d</mi> <mi>u</mi> </msub> <mo>+</mo> <msub> <mi>d</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> </math> Second Zagreb Index (M2): <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>G</mi> <mo>)</mo> <mo>=</mo> <munder> <mo>&sum;</mo> <mrow> <mi>u</mi> <mi>v</mi> <mo>&#x2208;</mo> <mi>E</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </munder> <mo>(</mo> <msub> <mi>d</mi> <mi>u</mi> </msub> <mo>&times;</mo> <msub> <mi>d</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> </math> In this paper, we explore several degree-reverse Revan reduced reverse leap eccentricity-based first, second, third, fourth, and fifth Zagreb indices of honeycomb networks. Additionally, we investigate the degree-based Zagreb indices of the line graph of the subdivision graph of honeycomb networks.