We call a Cayley digraph X = Cay(G, S) normal for G if the right regular representation of G is normal in the full automorphism group Ant(X) of X. In this paper, we give a classification of all nonnormal Cayley graphs...We call a Cayley digraph X = Cay(G, S) normal for G if the right regular representation of G is normal in the full automorphism group Ant(X) of X. In this paper, we give a classification of all nonnormal Cayley graphs of finite abelian groups with valency 5.展开更多
This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating s...This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating since the agents may be resource-limited in many real systems. The discrete time instants where the events are triggered are determined by a trigger function with respect to a certain measurement error. A centralized average-consensus protocol is proposed first for networks with fixed interaction topology, the stability and influencing factors of which are also analyzed. The design of trigger functions for networks with variable topology is also discussed. Then the results are extended to the decentralized counterpart, in which agents require only the information of their neighbors. Numerical examples are also provided that demonstrate the effectiveness of the theoretical results.展开更多
The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It ...The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.展开更多
基金KOSEF Grant 96-0701-03-01-3, and also by the National Natural ScienceFoundation and the Postdoctoral Science Foundation of Chi
文摘We call a Cayley digraph X = Cay(G, S) normal for G if the right regular representation of G is normal in the full automorphism group Ant(X) of X. In this paper, we give a classification of all nonnormal Cayley graphs of finite abelian groups with valency 5.
基金supported by the National Natural Science Foundation of China under Grant No.60904064, 61174094the Program for New Century Excellent Talents in University of China(NCET-10-0506)the Tianjin Natural Science Foundation of China under Grant No.09JCYBJC01700
文摘This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating since the agents may be resource-limited in many real systems. The discrete time instants where the events are triggered are determined by a trigger function with respect to a certain measurement error. A centralized average-consensus protocol is proposed first for networks with fixed interaction topology, the stability and influencing factors of which are also analyzed. The design of trigger functions for networks with variable topology is also discussed. Then the results are extended to the decentralized counterpart, in which agents require only the information of their neighbors. Numerical examples are also provided that demonstrate the effectiveness of the theoretical results.
文摘The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.
