Browsing by Author "Raman S."

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    Domination integrity and efficient fuzzy graphs
    (Springer, 2020) Mariappan S.; Ramalingam S.; Raman S.; Bacak-Turan G.
    In this paper, domination integrity of fuzzy graph and efficient fuzzy graph concepts is introduced with examples. An algorithm is developed to find whether an arc is strong or not. If it is strong, another algorithm will classify it as α strong arc and β strong arc. The next algorithm is used to find whether the given fuzzy graph is a fuzzy tree or not. Domination and integrity are two different parameters used to define the stability of a graph in various situations. Using the strong arc concept a new parameter, domination integrity is defined and lower and upper bounds are found. This paper discusses the domination integrity for standard graphs such as path, cycle and complete graph. The domination integrity for Cartesian product of fuzzy graphs is also discussed. Finally, the new class of fuzzy graph, efficient fuzzy graph, is introduced. Efficient fuzzy graph is a special type of fuzzy graph that has the same dominating set, other than vertex set V, for both fuzzy graph and its underlying crisp graph. © 2019, Springer-Verlag London Ltd., part of Springer Nature.
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    Vulnerability of sewer network – graph theoretic approach
    (Desalination Publications, 2020) Ganesan B.; Raman S.; Ramalingam S.; Turan M.E.; Bacak-Turan G.
    One of the most important structures in urban areas is an efficient sewer system to protect humans and the environment from the detrimental effects of wastewater. Such sewer systems often consist of pipes, manholes, pumping stations, and other complementary units. Strict monitoring of the sewer system is highly essential as any leakage can cause undesirable effects on health and safety. The layout is modeled as a graph which contains all sewer links and satisfies all the restrictions of a sanitary sewer system. In this work, we apply centrality measures on the sewer network system and water distribution system and also analyze the vulnerability of these systems. © 2020 Desalination Publications. All rights reserved.