Generalized stepwise transmission irregular graphs

The transmission ${\rm Tr}_G(u)$ of a vertex $u$ of a connected graph $G$ is the sum of distances from $u$ to all other vertices. $G$ is a stepwise transmission irregular (STI) graph if $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= 1$ holds for any edge $uv\in E(G)$. In this paper, generalized STI graphs are introduced as the graphs $G$ such that for some $k\ge 1$ we have $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= k$ for any edge $uv$ of $G$. It is proved that generalized STI graphs are bipartite and that as soon as the minimum degree is at least $2$, they are 2-edge connected. Among the trees, the only generalized STI graphs are stars. The diameter of STI graphs is bounded and extremal cases discussed. The Cartesian product operation is used to obtain highly connected generalized STI graphs. Several families of generalized STI graphs are constructed

The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

Improving Genetic Algorithms with Solution Space Partitioning and Evolution Refinements

[[abstract]]Irregular sum problem (ISP) is an issue resulted from mathematical problems and graph theories. It has the characteristic that when the problem size is getting bigger, the space of the solution is also become larger. Therefore, while searching for the feasible solution, the larger the question the harder the attempt to come up with an efficient search. We propose a new genetic algorithm, called the Incremental Improving Genetic Algorithm (IIGA), which is considered efficient and has the capability to incrementally improve itself from partial solutions. The initial solutions can be constructed by satisfying the constraints in stepwise fashion. The effectiveness of IIGA also comes from the allowing of suitable percentage of illegal solutions during the evolution for increasing the effectiveness of searching. The cut-point of the genetic coding for generating the descendants has carefully planned so that the algorithm can focus on the key factors for the contradiction and has the chances to fix it. After comparing the results of IIGA and usual genetic algorithm among different graphs, we found and shown that the performance of IIGA is truly better.[[conferencetype]]國際[[conferencedate]]20070824~20070827[[iscallforpapers]]Y[[conferencelocation]]Haikou, Chin