32475390
k-Cycle resonant graphs
Abstract A connected graph G is said to be k -cycle resonant if, for 1 ⩽ t ⩽ k , any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. In this paper, we at the first time introduce the concept of k -cycle resonant graphs, and investigate some properties of k -cycle resonant graphs. Some simple necessary and sufficient conditions for a graph to be k -cycle resonant are given. The construction of k -cycle resonant hexagonal systems are also characterized.
45999842
The number of spanning trees in odd valent circulant graphs
In this paper, we consider the number of spanning trees in circulant graphs. For any class of odd valent circulant graphs C"2"n(a"1,a"2,...,a"k"-"1,n), where a"1,a"2,...,a"k"-"1 are fixed jumps and n varies, some formulas, asymptotic behaviors and linear recurrence relations for the number of its spanning trees are obtained, and some known results on the ones in even valent circulant graphs C"n(a"1,a"2,...,a"k) are improved.
205056734
Hamiltonicity of a Type of Interchange Graphs
Abstract Let R(r1,…, rm) and S(s1,…, sn) be two nonnegative integral vectors, and let U (R,S) denote the class of all m×n matrices of 0's and 1's having row sum vector R and column sum vector S. We prove that if s1s2⋯sn1, the interchange graph G(R,S) of U (R,S) is hamiltonian.
5788058
Heredity of the index of convergence of the line digraph
Let D be a digraph, and let Ln(D) and k(D) denote the nth iterated line digraph of D and the index of convergence of D, respectively. We prove that if D contains neither sources nor sinks, then: (1) k(Ln(D))=k(D)=0 if every connected component of D is a directed cycle. (2) k(Ln(D))=k(D)+n if there exists at least one connected component of D that is not a directed cycle. Finally, we prove that if D has no sources or no sinks then k(D) ≤ k(L(D)) ≤ k(D)+1.
204989114
On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs
Abstract In this paper, we give the spectra and characteristic polynomials of generalized de Bruijn graphs. By Tutte's Theorem we can obtain the number of spanning trees and the number of Eulerian tours in such graphs.
46002685
3-Restricted Edge Connectivity Of Vertex Transitive Graphs
29766053
Construction for bicritical graphs and k-extendable bipartite graphs
A graph G is said to be bicritical if G-u-v has a perfect matching for every choice of a pair of points u and v. Bicritical graphs play a central role in decomposition theory of elementary graphs with respect to perfect matchings. As Plummer pointed out many times, the structure of bicritical graphs is far from completely understood. This paper presents a concise structure characterization on bicritical graphs in terms of factor-critical graphs and transversals of hypergraphs. A connected graph G with at least 2k+2 points is said to be k-extendable if it contains a matching of k lines and every such matching is contained in a perfect matching. A structure characterization for k-extendable bipartite graphs is given in a recursive way. Furthermore, this paper presents an O(mn) algorithm for determining the extendability of a bipartite graph G, the maximum integer k such that G is k-extendable, where n is the number of points and m is the number of lines in G.
34749580
Plane elementary bipartite graphs
A connected graph is called elementary if the union of all perfect matchings forms a connected subgraph. In this paper we mainly study various properties of plane elementary bipartite graphs so that many important results previously obtained for hexagonal systems are treated in a unified way. Firstly, we show that a plane bipartite graph G is elementary if and only if the boundary of each face (including the infinite face) is an alternating cycle with respect to some perfect matching of G. For a plane bipartite graph G all interior vertices of which are of the same degree, a stronger result is obtained; namely, G is elementary if and only if the boundary of the infinite face of G is an alternating cycle with respect to some perfect matching of G. Second, the concept of the Z-transformation graph Z(G) of a hexagonal system G (whose vertices represent the perfect matchings of G) is extended to a plane bipartite graph G and some results analogous to those for hexagonal systems are obtained. A peripheral face f of G is called reducible if the removal of the internal vertices and edges of the path that is the intersection of f and the exterior face of G results in a plane elementary bipartite graph. Thirdly, we obtain the reducible face decomposition for plane elementary bipartite graphs. Furthermore, sharp upper and lower bounds for the number of reducible faces are derived. Conversely, we can construct any plane elementary bipartite graphs by adding new peripheral faces one by one. As applications of this approach, we give simple construction methods for several types of plane elementary bipartite graphs G that contain a forcing edge (which belongs to exactly one perfect matching of G) and whose Z-transformation graphs Z(G) contain vertices of degree one.
9404547
Blocking-aware processor voltage scheduling for real-time tasks
As mobile computing is getting popular, there is a growing need for techniques that minimize energy consumption on battery-powered mobile devices. Processor voltage scheduling can effectively reduce processor energy consumption by lowering the processor speed. In this paper, we study voltage scheduling for real-time periodic tasks with non-preemptible sections. Three schemes are proposed: The static speed algorithm derives the minimum static feasible speed based on the stack resource policy. Due to blocking, this static speed is usually higher than the speed required for scheduling fully preemptible tasks (called the utilization speed). Two dynamic speed algorithms are then introduced to further reduce energy consumption. The novel dual speed algorithm operates the processor at the utilization speed whenever possible and switches to the higher static speed only when blocking occurs. The dual speed dynamic reclaiming algorithm reserves time budget for each job, reclaims the unused time budget from completed jobs and redistributes it to subsequent jobs so they can run at a lower speed whenever possible. Feasibility conditions for real-time task sets have been derived and proved mathematically. Simulation results show that the proposed voltage scheduling algorithms dramatically reduce processor energy consumption over non-power-aware scheduling algorithms. Furthermore, the two dynamic speed algorithms consistently outperform the static speed scheme in a wide range of system and workload conditions.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
30156477
Examination of load-balancing methods to improve efficiency of a composite materials manufacturing process simulation under uncertainty using distributed computing
Process simulations play an important role in guiding process understanding and development, without requiring costly manufacturing trials. For process design under uncertainty, a large number of simulations is needed for an accurate convergence of the moments of the output distributions, which renders such stochastic analysis computationally intensive. This paper discusses the application of a basic distributed computing approach to reduce the computation time of a composite materials manufacturing process simulation under uncertainty. Specifically, several load-balancing methods are explored and analyzed to determine the best strategies given heterogeneous tasks and heterogeneous networks, especially when the individual task times cannot be predicted.