The general sum-connectivity index of a graph G is χα(G) = ∑ uv∈E(G) (d(u)+d(v)), where d(u) denotes the degree of vertex u ∈ V (G), and α is a real number. In this paper, we show that in the class of graphs G of order n ≥ 3 and minimum degree δ(G) ≥ 2, the unique graph G having minimum χα(G) is K2 + Kn−2 if −1 ≤ α < α0 ≈ −0.867. Similarly, if we impose the supplementary condition for G to be t...

Multi-agent games are becoming an increas­ ingly prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic market­ places makes the study of computationally simple agents an appealing direction. In this work, we analyze the behavior of agents that incrementally adapt their strategy through gradi...

My primary research interest is social behavior for software agents to achieve cooperation in general-sum normal form games. An agent can easily be programmed to constantly cooperate in a normal form game, but such an agent is not suitable for environments with potentially hostile opponents. For a rational agent, the main reason to cooperate is to induce reciprocation therefore it is necessary ...

Stochastic games are a generalization of MDPs to multiple agents, and can be used as a framework for investigating multiagent learning. Hu and Wellman (1998) recently proposed a multiagent Q-learning method for general-sum stochastic games. In addition to describing the algorithm, they provide a proof that the method will converge to a Nash equilibrium for the game under specified conditions. T...

Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalit...

A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks in the lattice, and an interpretation of these worldsheets as spacetime geometries is given, based on the geometry defined by spin networks in canonical loop quantized GR. The spacetime g...

In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

An important subclass of the min-sum labeling problem (also known as discrete energy minimization or valued constraint satisfaction) is the pairwise min-sum problem with arbitrary unary costs and attractive Potts pairwise costs (also known as the uniform metric labeling problem). In analogy with our recent result, we show that solving the LP relaxation of the Potts min-sum problem is not signif...

*Correspondence: [email protected] 1School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan 2Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract Let G be a connected graph. The degree of...