The Zagreb-coindex of Four Operations on Graphs

Fuzzy Optimization and Modeling Journal

دوره 2، شماره 2، تیر 2021، صفحه 41-45   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/fomj.2021.1931773.1030

نویسنده

Mobina Ghorbaninejad^*

Department of Mathematics, Allame Tabarsi Institute, Qaemshahr, Iran

چکیده

In 1972, within a study of the structure-dependency of total π-electron energy (E), it was shown that E depends on the sum of squares of the vertex degrees of the molecular graph (later named first Zagreb index), and thus provides a measure of the branching of the carbon-atom skeleton. Topological indices are found to be very useful in chemistry, biochemistry and nanotechnology in isomer discrimination, structure–property relationship, structure-activity relationship and pharmaceutical drug design. In chemical graph theory, a topological index is a number related to a graph which is structurally invariant. One of the oldest most popular and extremely studied topological indices are well–known Zagreb indices. In a (molecular) graph G, the Zagreb topological index is equal to the sum of squares of the degrees of vertices of G and the Zagreb coindex is defined as the sum of a graph’s vertex degrees which is not adjacent. In this paper, we obtain the Zagreb coindex of four operations on graphs.

کلیدواژه‌ها

Graph؛ Zagreb–index؛ F–sum؛ Zagreb-coindex