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Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.

We give a unified approach to analysing, for each positive integer s, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s-arc transitive graphs of diameter at least s. A graph is in the class if it is connected and if, for each vertex v, the subgroup of automorphisms fixing v acts transitively on the set of vertices at distance i from v, ...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

In this paper, a gentle introduction to Game Theory is presented in the form of basicconcepts and examples. Minimax and Nash's theorem are introduced as the formalde nitions for optimal strategies and equilibria in zero-sum and nonzero-sum games.Several elements of cooperative gaming, coalitions, voting ensembles, voting power andcollective e ciency are described in brief. Analy...

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually st...

We present a concurrent Completion procedure based on the use of a SOUR graph as data structure. The procedure has the following characteristics. It is asynchronous, there is no need for a global memory or global control, equations are stored in a SOUR graph with maximal structure sharing, and each vertex is a process, representing a term. Therefore, the parallelism is at the term level. Each e...