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Connectivity measures real energization state of manifold applications and user interference in many criteria-based network systems. Randic index is a parameter of this type that can be used to measure the combined power of molecular graph or graphical network system. The concept of Randic index has been applied in a connected system in Indonesia tourism sectors under some uncertain conditions. First, Randic index of fuzzy graph (FG) and fuzzy subgraph are introduced and investigated their properties. Second, different upper and lower bounds of Randic index and their isomorphic properties in fuzzy graphs are exhibited. Third, the Randic index in directed fuzzy graph (FDG) is introduced. Due to presence of similar contribution of vertices, many formulas for calculating Randic index of regular fuzzy graphs are presented. Fourth, some similarity and distinction of Randic index with connectivity index (CI) and Wiener index (WI) in fuzzy graph are analyzed. Fifth, an algorithm and a flowchart are proposed to determine Randic index in a fuzzy graph. Finally, an application is depicted to mention the order of important crossroads and stoppages between Balai Kemambang (BKB) and Bukit Kendalisada (BKS) in Indonesia tourism sectors. [ABSTRACT FROM AUTHOR]

In this paper, we have extended the formula of fuzzy chromatic number (FCN) for the non-disjoint union of two fuzzy graphs. Further, we constructed an algorithm based on the FCN for determining a fuzzy phase system in order to coordinate traffic flow of two paired intersections. By combining the fuzzy phase system and the fuzzy inference system, we were able to construct another algorithm to determine all possible phase timings for coordinating the intersections. Performance of the algorithms was evaluated through a case study at two intersections in Semarang City, Indonesia. The results showed that the proposed phase and timing systems for the two paired intersections could reduce the red and cycle times compared with the control of two intersections separately. The present findings might serve as a feasible proposal for congestion problems in any paired intersections. [ABSTRACT FROM AUTHOR]