Zagreb Connection Indices of Molecular Graphs Based on Operations

Abstract

Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol. Inform. 372018,1−7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

Study of Carbon Nanocones CNC k n Asif1, Hussain2, Almohamedh3 et al. 2021Mathematical Problems in Engineering8020View full textAdd to dashboardCite

“…In this work, we use graph theoretic techniques adopted in [21][22][23][24][25] to study the topology of the corresponding molecular graph of underlying compound for their insight investigation. We used investigative procedure, vertex segment strategy, edge segment procedure, and degree tallying strategy along with combinatorial enlisting techniques, number theoretic logics, and edges and vertices partition according to the values associated to the vertices for desired computation.…”

“…Ali et al [20] concluded that ZC * 1 has correlation coefficient approximately 0.949 and 0.892 for acentric factor and entropy, respectively, and ZC 1 has a good correlation with enthalpy. Javaid et al studied T-sum graphs and graphs constructed through graph operation using connection indices [21][22][23][24][25].…”

Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

“…Ali et al [31] computed the analysis of Zagreb connection indices and coindices for some chemical structures of operations on graphs. For further studies and properties of the Zagreb connection indices, we refer to [32][33][34][35][36][37][38][39][40]. Recently, Gong et al [41,42] developed blocking lot-streaming flow shop scheduling problems and dynamic interval multiobjective optimization problems.…”

Topological Indices and f-Polynomials on Some Graph Products

“…The zigzag polyhex nanotube TUHC 6 [2n, 2] is the generalized hierarchical product of the path graph P 2 and the cycle graph C 2n . See [46,47].…”