The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph which was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced. In this paper we study the F-index of four operations on graphs which were introduced by Eliasi and Taeri [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math.157...

Topological indices are numbers that applied to a graph and can be used describe specific properties through algebraic structures. Algebraic theory is helpful tool in range of chemistry domains. Because it helps explain how the different symmetries molecules crystals affect their structure dynamics, powerful theoretical approach for forecasting both common uncommon characteristics molecules. A ...

For a (molecular) graph, the multiplicative Zagreb indices ∏ 1-index and ∏ 2index are multiplicative versions of the ordinary Zagreb indices (M1-index and M2index). In this note we report several sharp upper bounds for ∏ 1-index in terms of graph parameters including the order, size, radius, Wiener index and eccentric distance sum, and upper bounds for ∏ 2-index in terms of graph parameters inc...

Several different topological indices (the carbon number, the Wiener index, the Balaban dis­ tance sum connectivity index, the Randic molecular identification number, and the Randic molecular connectivity indices °/, 2%, 3̂ p and 3/ c) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published so...

The relationship between the Randic , Wiener, Hosoya , Balaban, Schultz indices, Harary numbers andDistance matrix to enthalpies of formation (Airf), heat capacity, (Cp) , enthalpies of combustion (AH °c ),enthalpy of vaporization (AH °vap) and normal boiling points (bpK)of C2 C10 normal alkanes isrepresented

Recently, D. Vukičević and J. Sedlar in [1] introduced an order “⪯” on Tn, the set of trees n vertices, such that topological index F a graph is function defined 〈Tn,⪯〉. It provides new approach to determine extremal graphs with respect F. By using method they determined common maximum and/or minimum Tn indices Wiener type anti-Wiener type. Motivated by their researches we further study 〈Tn,⪯〉 ...

A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based indices such as Wiener index, hyper-Wiener Harary Tratch – Stankevitch Zefirov index. In present study, we determine closed form for third type chain hex-derived network dime...

the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...