Suppose there is a simple, and finite graph G = (V, E). The coloring of vertices c is denoted by c: E(G) → {1,2, ..., k} with k is the number of rainbow colors on graph G. A graph is said to be rainbow connected if every pair of points x and y has a rainbow path. A path is said to be a rainbow if there are not two edges that have the same color in one path. The rainbow connected number of graph G denoted by rc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. Furthermore, a graph is said to be connected to rainbow vertex if at each pair of vertices x and y there are not two vertices that have the same color in one path. The rainbow vertex connected to the number of graph G is denoted by rvc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. This paper discusses rainbow vertex-connected numbers in the amalgamation of a diamond graph. A diamond graph with 2n points is denoted by an amalgamation of a diamond graph by adding the multiplication of the graph t at point v is denoted by Amal (Brn,v,t).
Coronary heart disease (CHD) is caused by various reasons. One of the main causes of coronary heart disease is cholesterol. Cholesterol comes from two sources, namely, that which is produced by the liver and through the food consumed. This article discusses the mathematical model of coronary heart disease which refers to the SEI (Susceptible-exposed-infected) model, with modifications in the form of the addition of the recovered (R) variable and parameters in the form of a healthy lifestyle and surgery. Hereinafter this model is called the SEIR (Susceptible-Exposed-Infected-Recovered) model. This study aims to determine the problem of coronary heart disease in cholesterol sufferers and to analyze the effect of operating parameters and a healthy lifestyle on the patient's healing (R) is higher than the opportunity value of the other groups. And the opportunity value of an infected individual is much lower than that of other groups. This shows that the chances of recovery for people with coronary heart disease with a high operating route.
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