Extremal polyomino chains with respect to general Randić index

For a (molecular) graph \(G,\) the general Randi? index \(R_{\alpha }(G)\) is defined as the sum of the weights \([d_{u}d_{v}]^{\alpha }\) of all edges \(uv\) of \(G,\) where \(d_{u}\) (or \(d_{v}\)) denotes the degree of a vertex \(u\) (or \(v\)) in \(G\) and \(\alpha \) is an arbitrary real number. In this paper, we give an efficient formula for computing the general Randi? index of polyomino chains and characterize the extremal polyomino chains with respect to this index, which generalizes one of the main results in (Yarahmadi et al. Appl Math Lett 25:166–171, 2012).     

Fibonacci index and stability number of graphs: a polyhedral study

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study by establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order n.     

What is the leanness level of your organisation in lean transformation implementation? An integrated lean index using ANP approach

We develop a lean index to assess the leanness level of the organisation in sustaining lean transformation. This ‘lean index’ is developed from theory, and is quantified using a multi-criteria approach i.e., analytic network process (ANP). This index provides a useful measure for sustainable lean performance because it adopts a holistic approach of performance measurement based on the socio-technical perspective which considers the interdynamics of human, system and technology.