Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties, such as melting and boiling points, toxicity and resistance. Here we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees and the Collat...

Ernesto Estrada Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is zero. On the basis of empirical analysis it is conclud...

Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...

Model Checking of tccp programs Maŕıa Alpuente 1 ,2 Maŕıa del Mar Gallardo 1 ,3 Ernesto Pimentel ,4 Alicia Villanueva 1 ,5

We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker.

Marta Coll*, Chiara Piroddi, Jeroen Steenbeek, Kristin Kaschner, Frida Ben Rais Lasram, Jacopo Aguzzi, Enric Ballesteros, Carlo Nike Bianchi, Jordi Corbera, Thanos Dailianis, Roberto Danovaro, Marta Estrada, Carlo Froglia, Bella S. Galil, Josep M. Gasol, Ruthy Gertwagen, João Gil, François Guilhaumon, Kathleen Kesner-Reyes, Miltiadis-Spyridon Kitsos, Athanasios Koukouras, Nikolaos Lampadariou, ...