Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). Total k-labeling is a function fe from the edge set to the first ke natural number, and a function fv from the vertex set to the non negative even number up to 2kv, where k = max{ke , 2kv }. An edge irregular reflexive k labeling of the graph G is the total k-labeling, if for every two different edges x 1 x 2 and x 1 ′ x 2 ′ of G , w t ( x 1 x 2 ) ≠ w t ( x 1 ′ x 2 ′ ) , where w t ( x 1 x 2 ) = f v ( x 1 ) + f e ( x 1 x 2 ) + f v ( x 2 ) . The minimum k for graph G which has an edge irregular reflexive k-labelling is called the reflexive edge strength of the graph G, denoted by res(G). In this paper, we determined the exact value of the reflexive edge strength of family trees, namely generalized sub-divided star graph, broom graphs, and double star graph.

This paper proposes an image processing approach to identify Gram-negative bacteria. Gram-negative bacteria are one of the bacteria that cause lung lobe damage-bacterial samples obtained through smears of the patient's sputum. The first step bacterium should pass the pathogen test process. After that, it bred using Mc Conkey's media. The problem faced is that the process of identifying bacterial objects is still done manually under a fluorescence microscope. The contributions offered from this research are focused on observing bacterial morphology for the operation of selecting shape features. The proposed method is a convolutional neural network with fine-tuning. In the stages of the process, a convolutional neural network of the VGG-16 architecture used dropout, data augmentation, and fine-tuning stages. The main goal of the current research was to determine the method selection is to get a high degree of accuracy. This research uses a total sample of 2520 images from 2 different classes. The amount of data used at each stage of training, testing, and validation is 840 images with dimensions of 256x256 pixels, a resolution of 96 points per inch, and a depth of 24 bits. The accuracy of the results obtained at the training stage is 99.20%.

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Data classification has several problems one of which is a large amount of data that will reduce computing time. SVM is a reliable linear classifier for linear or non-linear data, for large-scale data, there are computational time constraints. The Fractional gradient descent method is an unconstrained optimization algorithm to train classifiers with support vector machines that have convex problems. Compared to the classic integer-order model, a model built with fractional calculus has a significant advantage to accelerate computing time. In this research, it is to conduct investigate the current state of this new optimization method fractional derivatives that can be implemented in the classifier algorithm. The results of the SVM Classifier with fractional gradient descent optimization, it reaches a convergence point of approximately 50 iterations smaller than SVM-SGD. The process of updating or fixing the model is smaller in fractional because the multiplier value is less than 1 or in the form of fractions. The SVM-Fractional SGD algorithm is proven to be an effective method for rainfall forecast decisions.