Sciences mathématiques, No 31 GRAPHS WITH LEAST EIGENVALUE −2 ATTAINING A CONVEX QUADRATIC UPPER BOUND FOR THE STABILITY NUMBER

Bulletin T.CXXXIII de l’Académie serbe des sciences et des arts − 200

Graphs with Given Diameter Maximizing the Spectral Radius (Revision of Center Discussion Paper 2006-105)

We determine the graphs with maximal spectral radius among the ones on n nodes with diameter D.

Matrices and Graphs

The present article is designed to be a contribution to the chapter `Combinatorial Matrix Theory and Graphs' of the Handbook of Linear Algebra, to be published by CRC Press. The format of the handbook is to give just definitions, theorems, and examples; no proofs. In the five sections given below, we present the most im- portant notions and facts about matrices related to (undirected) graphs. 1. Graphs. 2. The adjacency matrix and its eigenvalues. 3. Other matrix representations. 4. Graph parameters. 5. Association schemes.

The Cost of Segregation in Social Networks

This paper investigates the private provision of public goods in segregated societies. While most research agrees that segregation undermines public provision, the findings are mixed for private provision: social interactions, being strong within groups and limited across groups, may either increase or impede voluntary contributions. Moreover, although efficiency concerns generally provide a rationale for government intervention, surprisingly, little light is shed in the literature on the potential effectiveness of such intervention in a segregated society. This paper first develops an index based on social interactions, which, roughly speaking, measures the welfare impact of income redistribution in an arbitrary society. It then shows that the proposed index vanishes when applied to large segregated societies, which suggests an asymptotic neutrality of redistributive policies