General multi-sum transformations and some implications

Some new bounds on the general sum--connectivity index

Let $G=(V,E)$ be a simple connectedgraph with $n$ vertices, $m$ edges and sequence of vertex degrees$d_1 ge d_2 ge cdots ge d_n>0$, $d_i=d(v_i)$, where $v_iin V$. With $isim j$ we denote adjacency ofvertices $v_i$ and $v_j$. The generalsum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, where $alpha$ is an arbitrary real<b...

Some Bounds on General Sum Connectivity Index

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

Policy Invariance under Reward Transformations for General-Sum Stochastic Games

We extend the potential-based shapingmethod fromMarkov decision processes to multi-player general-sum stochastic games. We prove that the Nash equilibria in a stochastic game remains unchanged after potential-based shaping is applied to the environment. The property of policy invariance provides a possible way of speeding convergence when learning to play a stochastic game.

Combinations and transformations of some general coalition-games

The general coalition-game model suggested in [2] is considered, and a few types of combinations and transformations of such games are investigated. It is shown that a conjunction, disjunction, and combination of two general coalition-games is, under natural conditions, also a general coalition-game. Also the main relations between the solutions of the original games and the resulting one are d...

On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes