Applications of maximum matching by using bipolar fuzzy incidence graphs.

The extension of bipolar fuzzy graph is bipolar fuzzy incidence graph (BFIG) which gives the information regarding the effect of vertices on the edges. In this paper, the concept of matching in bipartite BFIG and also for BFIG is introduced. Some results and theorems of fuzzy graphs are also extended in BFIGs. The number of operations in BFIGs such as augmenting paths, matching principal numbers, relation between these principal numbers and maximum matching principal numbers are being investigated which are helpful in the selection of maximum most allied applicants for the job and also to get the maximum outcome with minimum loss (due to any controversial issues among the employees of a company). Some characteristics of maximum matching principal numbers in BFIG are explained which are helpful for solving the vertex and incidence pair fuzzy maximization problems. Lastly, obtained maximum matching principal numbers by using the matching concept to prove its applicability and effectiveness for the applications in bipartite BFIG and also for the BFIG.

Intradermal application of tranexamic acid (TA) as treatment of melasma in the out-patients department of a public sector hospital: A pilot study.

The effect of intradermal TA on melasma was evaluated as a possible treatment modality on all of the 11 patients (fitting the inclusion criteria) presenting in the out-patient department of the Benazir Bhutto Hospital, Rawalpindi during Sep 2019 to Mar 2020. Their pre- and post-interventional results were evaluated after being injected with 4 mg/ml of TA on the lesions once weekly for 6 weeks, using Wilcoxon signed rank test in SPSS v 24. The average duration of melasma in our patients was 25.3±7.6 in months. The mean modified MASI score rating was 12.2 (2.3) and 5.1 (1.4) before and after intervention with intradermal TA respectively. The largest difference obtained in the mMASI scores of the patients was 10.8. TA has a distinctive effect as a treatment modality for melasma, as it is easily employable with very few side effects.

Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.

A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from vertex b to vertex a is always same. But if someone is interested in finding CC from vertex a to an edge ab, then graphs and FGs cannot answer this question. Therefore, in this research article, we proposed the idea of CC for FIG. Because in FIG, we can find CC from vertex a to vertex b and also from vertex a to an edge ab. Also, we proposed the idea of CC of fuzzy incidence cycles (FICs) and complete fuzzy incidence graphs (CFIGs). The fuzzy incidence cyclic cut-vertex, fuzzy incidence cyclic bridge, and fuzzy incidence cyclic cut pair are established. A condition for CFIG to have fuzzy incidence cyclic cut-vertex is examined. Cyclic connectivity index and average cyclic connectivity index of FIG are also investigated. Three different types of vertices, such as cyclic connectivity increasing vertex, cyclically neutral vertex and, cyclic connectivity decreasing vertex, are also defined. The real-life applications of CC of FIG in a highway system of different cities to minimize road accidents and a computer network to find the best computers among all other computers are also provided.