We formally introduce in this paper two parameters graph theory, namely, clique centrality and global centrality. Let G be a finite, simple undirected of order n. A is nonempty subset W \(\subseteq\) V (G) such that the subgraph \(\langle\)W\(\rangle\)G induced by complete. The maximum size any containing vertex u \(\in\) called G. Normalizing sum centralities all vertices will lead us to G, wh...

Given a graph G with source and destination vertices s , t ? V ( ) respectively, Tracking Paths asks for minimum set of T ? such that the sequence restricted to encountered in each simple path from is unique. The problem was proven NP -hard [3] found admit quadratic kernel when parameterized by size desired solution [8] . Following recent trends, first time, we study respect structural paramete...

Iterated clique graphs arise when the clique operator is applied to a graph more than once. Determining whether a graph is a clique graph or an iterated clique graph is usually a difficult task. The fact that being a clique graph and being an iterated clique graph are not equivalent things has been proved recently. However, it is still unknown whether the classes of second iterated clique graph...

We construct multi-prover proof systems for NP which use only a constant number of provers to simultaneously achieve low error, low randomness and low answer size. As a consequence, we obtain asymptotic improvements to approximation hardness results for a wide range of optimization problems including minimum set cover, dominating set, maximum clique, chromatic number, and quartic programming; a...

We present a model for the vehicle and crew scheduling problem in urban public transport systems by combining models for vehicle and crew scheduling that cover a great variety of real world aspects, especially constraints for crews resulting from wage agreements and internal regulations. The main part of the model consists of a set partitioning formulation to cover the desired trips of the sche...

We consider a graph whose vertices are legally colored using k colors and ask if the contains -clique. As it turns out this very special type of -clique problem is in an intimate connection with constructing schedules. The practicality clique search based construction schedules checked by carrying numerical experiments.

A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of th...