ABSTRACT
Let G be a connected graph with vertices V and edges E. Rubbling is a recent development in graph theory and combinatorics. In graph rubbling an extra shift is allowed that adds a pebble at a node after the deletion of one pebble each at two neighbouring vertices. For the first time, we introduce the concept of monophonic rubbling numbers into the literature. A monophonic rubbling number, µ r ( G ) , is the least number m required to ensure that any vertex is reachable from any pebble placement of m pebbles using a monophonic path by a sequence of rubbling shifts. We calculate the upper bound and lower bound using the monophonic rubbling number of some standard graphs and derived graphs.
ABSTRACT
In this computer world, huge data are generated in several fields. Statistics in the healthcare engineering provides data about many diseases and corresponding patient's information. These data help to evaluate a huge amount of data for identifying the unknown patterns in the diseases and are also utilized for predicting the disease. Hence, this work is to plan and implement a new computer-aided technique named modified Ensemble Learning with Weighted RBM Features (EL-WRBM). Data collection is an initial process, in which the data of various diseases are gathered from UCI repository and Kaggle. Then, the gathered data are pre-processed by missing data filling technique. Then, the pre-processed data are performed by deep belief network (DBN), in which the weighted features are extracted from the RBM regions. Then, the prediction is made by ensemble learning with classifiers, namely, support vector machine (SVM), recurrent neural network (RNN), and deep neural network (DNN), in which hyper-parameters are optimized by the adaptive spreading rate-based coronavirus herd immunity optimizer (ASR-CHIO). At the end, the simulation analysis reveals that the suggested model has implications to support doctor diagnoses.
