Thirty Essays on Geometric Graph Theory

Focus on the weakness of modeling WSN topology by the means of random graph theory, a new weighted topology model of WSN based on random geometric theory is proposed in this paper. For the proposed new network model, the weighting scheme of network edge take into account the property of distance decreasing effect for communication signal. It also defines the differential weight which can embody the energy consumption for network communication. Based on simulations and calculations of the measures for the network topology as well as comparison with other forms of network, the results indicate that the proposed network topology model can not only describe the interrelated connected relationship between different nodes but also verify the degree of node is subject to Poisson distribution. It also has prominent clustering effects. These properties are consist with real world networks.

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A Study on Slope Number of Certain Classes of Bipartite Graphs

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.10.21036 ◽

2018 ◽

Vol 7 (4.10) ◽

pp. 440

Author(s):

A. A. Antony mary ◽

A. Amutha ◽

M. S. Franklin Thamil Selvi

Keyword(s):

Graph Theory ◽

Information Visualization ◽

Optimization Problem ◽

Graph Drawing ◽

Quality Measures ◽

Bipartite Graphs ◽

Geometric Graph ◽

Structural Behavior ◽

Arbitrary Graph ◽

Number Problem

Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs creates one of the most intensively investigated classes of graphs, we consider few classes of graphs and discussed structural behavior of such graphs.

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