the zagreb indices are the oldest graph invariants used in mathematical chemistry to predictthe chemical phenomena. in this paper we define the multiple versions of zagreb indicesbased on degrees of vertices in a given graph and then we compute the first and secondextremal graphs for them.

Statistics is a science that provides precise techniques for collecting and sorting information made easy by tools and methods for further analysis. The object of descriptive statistics, from sample data, is to describe the most important characteristics, by which we refer to those amounts that provide information on the topic of interest which we are studying.

Context-free tree grammars, originally introduced by Rounds ((Rounds, 1970)), are powerful grammar devices for the definition of tree languages. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of monadic simple context-free tree languages. For this class of context-free tree languages, a faithful rendering of extended TAGs, we show that...

Acknowledgements : many thanks to professor Giovanni Pighizzini for its welcome and for having directed my internship. Many thanks also to Carlo Mereghetti and Beatrice Palano and all organizing committee of NCMA workshop for having given me the possibility to assist at this workshop. Many thanks also to Viliam Geffert for his contribution to our work. Thanks to Antonio Capoduro for coffees and...

For tabled Lindenmayer systems and their languages, the degree of synchronization and the degree of nondeterminism are well investigated measures of descriptional complexity. In this paper the sequential counterparts of tabled Lindenmayer systems, namely cooperating distributed grammar systems and their pure variant (working in the so called t-mode of derivation) are treated with respect to the...

In a designated verifier signature (DVS) scheme a signer creates a signature which is only verifiable by a designated verifier. A DVS is a useful scheme for authenticating a signer without disturbing her privacy. In a universal DVS (UDVS) scheme, everyone who holds Alice’s traditional signature on a message (the signature holder), is able to transform it to a DVS for a specific verifier. Non-de...

Decision tree pruning is critical for the construction of good decision trees. The most popular and widely used method among various pruning methods is cost-complexity pruning, whose implementation requires a training dataset to develop a full tree and a validation dataset to prune the tree. However, different pruned trees are found to be produced when the original dataset are randomly partitio...