Degree-Based Indices of Some Complex Networks
Lei Ding, Syed Ahtsham Ul Haq Bokhary, Masood Ur Rehman, Usman Ali, Hirra Mubeen, Quaid Iqbal, Jia‐Bao Liu
Abstract
A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph. Topological indices and physico-chemical properties such as atom-bond connectivity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mtext>ABC</a:mtext> </a:mrow> </a:mfenced> </a:math> , Randić, and geometric-arithmetic index <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mtext>GA</f:mtext> </f:mrow> </f:mfenced> </f:math> are of great importance in the QSAR/QSPR analysis and are used to estimate the networks. In this area of research, graph theory has been found of considerable use. In this paper, the distinct degrees and degree sums of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. Utilizing these edge partitions, the closed formulae for some degree-based topological indices of the networks are deduced.