Zhongxun Zhu

Tricyclic graph with maximal Estrada index

Let G be a simple connected graph on n vertices and λ 1 , λ 2 , ? , λ n be the eigenvalues of the adjacency matrix of G . The Estrada index of G is defined as E E ( G ) = ? i = 1 n e λ i . Let T n be the class of tricyclic graphs G on n vertices. In this paper, the graphs in T n with the maximal Estrada index is characterized.

A novel approach for bandwidth allocation among soft QoS traffic in wireless networks

The resource bandwidth allocation in a network is usually casted into a so-called network utility maximization NUM problem, which solution strategy has successfully generated distributed algorithms for congestion controlling of elastic traffic in a wire-lined network. However, for resource allocation of inelastic traffic including soft QoS quality of service traffic in a wireless network, this approach still faces challenges. First, it is hard for the wireless system to dynamically model the utility function of the users. Second, the utility function of soft QoS traffic is usually nonconcave, which brings the NUM optimization problem to be mathematically intractable. With deviation to the usual NUM theory, this paper proposes a novel optimization model and its algorithm to allocate bandwidth around the users desired value to the soft QoS traffic in a wireless network. Our approach takes advantage of the basic feature of soft QoS traffic; that is, it demands a preferred amount of bandwidth but allows some flexibility during normal operation. Compared with the utility-based approaches and solutions, our approach avoids the difficulty of finding the exact utility function expression for each user by using the preference bandwidth value. This facilitates the operation of real wireless networks. The proposed model and algorithm are verified by an example, which demonstrate better performance than the NUM approach.Copyright

The signless Laplacian spectral radius of bicyclic graphs with a given girth

Let B(n, g) be the class of bicyclic graphs on n vertices with girth g. In this paper, the graphs in B(n, g) with the largest signless Laplacian spectral radius are characterized.

Cacti with maximum eccentricity resistance-distance sum

Abstract The eccentricity resistance-distance sum of a connected graph G is defined as ξ R ( G ) = ∑ u , v ∈ V ( G ) ( e ( u ) + e ( v ) ) R ( u , v ) , where e ( u ) is the eccentricity of the vertex u and R ( u , v ) is the resistance distance between u and v in graph G . Let C a t ( n ; t ) be the set of all cacti possessing n vertices and t cycles. In this paper, some transformations of a connected graph are studied, which is mainly focused on the monotonicity on the eccentricity resistance-distance sum. By the transformation, the extremal graphs with maximum ξ R -value of C a t ( n ; t ) are characterized.

The number of independent sets of tricyclic graphs

Abstract Let T n be the class of tricyclic graphs G on n vertices. In this work, the graphs in T n with the smallest number of independent sets are characterized.

Output Feedback Assignability for Nonlinear Min-Max Systems

This paper investigates the output feedback cycle time assignability of the min-max systems which are more complex than the systems studied in recent years. Max-plus projection representation for the closed-loop system with min-max output feedback is introduced. The coloring graph is presented and applied to analyze the structure of systems effectively. The necessary and sufficient criterion for the output feedback cycle time assignability is established which is an extension of the results studied before. The methods are constructive in nature.