PELABELAN JUMLAH EKSKLUSIF PADA GRAF TANGGA Ln

Suatu graf terhubung disebut graf jumlah, sebagaimana yang dikemukakan oleh Harary [1] tahun 1990, jika terdapat suatu pelabelan jumlah L dari V ke himpunan bilangan bulat positif yang berbeda S; xy ∈ E jika dan hanya jika terdapat suatu simpul w∈V sedemikian sehingga berlaku L(w) = L(x) + L(y) ∈ S. Dalam kasus ini w disebut simpul bekerja. L menjadi pelabelan jumlah ekslusif jika graf G tidak mengandung simpul bekerja. Banyak minimum dari simpul terisolasi yang ditambahkan ke graf G sehingga labelnya eksklusif disebut bilangan jumlah eksklusif, dinotasikan dengan ε (G). Pada makalah ini akan ditunjukkan konstruksi pelabelan jumlah eksklusif graf tangga yang memilik ε (Ln) = 3 untuk n ≥ 3 Kata kunci: pelabelan jumlah eksklusif, graf tangg

Odd-even sum labeling in the context of duplication of graph elements

In this paper, odd-even sum labeling of the graphs obtained by duplication of graph elements of stars and paths are studie

On Sum Graphs over Some Magmas

We consider the notions of sum graph and of relaxed sum graph over a magma, give several examples and results of these families of graphs over some natural magmas. We classify the cycles that are sum graphs for the magma of the subsets of a set with the operation of union, determine the abelian groups that provide a sum labelling of $C_4$, and show that $C_{4\ell}$ is a sum graph over the abelian group $\mathbb{Z}_f\times\mathbb{Z}_f$, where $f=f_{2\ell}$ is the corresponding Fibonacci number. For integral sum graphs, we give a linear upper bound for the radius of matchings, improving Harary's labelling for this family of graphs, and give the exact radius for the family of totally disconnected graphs. We found integer labellings for the 4D-cube, giving a negative answer to a question of Melnikov and Pyatikin, actually showing that the 4D-cube has infinitely many primitive labellings. We have also obtained some new results on mod sum graphs and relaxed sum graphs. Finally, we show that the direct product operation is closed for strong integral sum graphs

Urban flood simulation and integrated flood risk management

Climate change induces the probability of occurring natural disasters; e.g. floods, Sea Level Rise, Green House Gases. Flood is considered one of the most dangerous phenomena that tremendously and dramatically threatening the human being and environment worldwide. Rapid urban growth, demographic explosion, and unplanned land uses have exacerbated the problem of urban flooding, particularly in the cities of China. In addition to that, the concept of flood risk management and adaptation measures and strategies are still missed in the cities’ development future plans. The main objective of this Ph.D. dissertation is to investigate the flood risk analysis and assessment based on flood simulation and adaptive strategies for flood event through two case studies of Changsha city in south-central China. In case study I, fluvial flooding was considered on mesoscale and an MCA-based approach was proposed to assess the integrated flood risk of Changsha central city. HEC-RAS 1-D model was used to simulation the inundation characteristics for hazard analysis based on four risk dimensions: economic, social, environmental, and infrastructural risk. For infrastructural dimension, apart for direct damage on road segments, network analysis method was combined with inundation information and macroscopic traffic simulation to evaluate the impact on traffic volume as well as a decrease of road service level. Closeness centrality weighted with a travel time of pre- and after- flood was compared in order to measure the impact on urban accessibility. Integrated risk values were calculated using various weighting criteria sets. Sobol' indices were used as a tool of spatially-explicit global Uncertainty Analysis and Sensitivity Analysis (UA/SA) for damage models. In case study II, an agent-based modeling approach was proposed to simulate the emergency pluvial flood event caused by a short-time rainstorm in local areas of cities aiming at developing an interactive flood emergency management system capable of interpreting the risk and reduction strategy of the pluvial flood. The simulation integrated an inundation model with microscopic traffic simulation. It also reveals that all agents can benefit significantly from both engineering measures and the only pedestrian obtain relatively more benefits from risk warning with high awareness. The method provided potentials in studies on the adaptive emergency management and risk reduction, help both decision-makers and stakeholders to acquire deeper and comprehensive understanding of the flood risk. This Ph.D. study has investigated holistic methods and models’ selection in flood risk assessment and management to overcome data deficiency and to achieve the integration of different data. The results of the first case study reveal that the integrated methods have proved to be able to improved flood risk analysis and assessment especially for indirect damage of infrastructural system with network features. The global UA/SA based on Sobol' method and visualization with maps enable to gain the spatial distribution of uncertainty for various factors, the validation of damage models, and deeper and more comprehensive understanding of flood risk. Then based on the integrated risk assessment, functions of spatial planning in flood risk management were discussed, potentially providing guidance and support for decision-making. The results of the second case study denote that agent-based modeling and simulation can be effectively utilized for flood emergency management. Two scenarios focusing on specific risk reduction interventions were designed and compared. Engineering measures by improving capability of the drainage system and the surface permeability of waterlogging areas are the most effective means for damage mitigation. High public risk awareness still has great potential benefits of the in the event of emergencies, which can greatly enhance the effectiveness of the official warning. The agent-based modeling and simulation provided an effective method for analyzing the effectiveness of different strategies for reducing flood risk at the local scale and for supporting urban flood emergency management. The case studies also indicate the significance and necessity of establishing a platform and database to realize full sharing and synergies of spatial information resources for flood risk management, which is a vital issue to manage the urban flood risk and take effective measures correspondingly with responding to emergency extreme flood event. Keywords: urban flood; flood risk assessment; network analysis; flood simulation; flood risk managemen