In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

In this paper, we consider upper bound graphs and double bound graphs of posets. We obtain a characterization of upper bound graphs whose complements are also upper bound graphs as follows: for a connected graph G, both G and G are upper bound graphs if and only if G is a split graph with V(G)= K + S, where K is a clique and S is an independent set, satisfying one of the following conditions: (...

In this paper, we analyze a bulk input Geom/Geom/1 queue with single working vacation. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived, from which we got the stochastic decomposition result for the PGF of the stationary queue size. It is important that we find the biparameter addition theorems of the conditional negative binomial distribu...

An algorithm recently developed by Enkhbat et al. [3] based on continuous relaxation of the quadratic assignment problem generates suboptimal solution of good quality on average giving no sufficient enough verification on global optimality of the generated solution, whereas a branch and bound method provides a solution with verified global optimality, taking on input an upper bound close to glo...

In this paper a Markov chain for contingency tables with two rows is defined. The chain is shown to be rapidly mixing using the path coupling method. We prove an upper bound for the mixing time of the chain. The upper bound is quadratic in the number of columns and linear in the logarithm of the table sum. By considering a specific problem, we prove a lower bound for the mixing time of the chai...

Fuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions areapproved and an upper bound for them are determined. Finally an algorithmis drawn to show theorems better.

Abstract: Focusing on incremental bulk metal forming processes, the indentation process is gaining interest as a fundamental part of these kinds of processes. This paper presents the analysis of the pressure obtained in indentation under the influence of different punch geometries. To this end, an innovative Upper Bound Theorem (UBT) based solution is introduced. This new solution can be easily...