The Zagreb indices were introduced by Gutman and Trinajstic in 1972. The K-Banhatti indices were introduced by Kulli in 2016. These two types of indices are closely related. In this study, we define the Zagreb- K-Banhatti index of a graph. We establish some relations between Zagreb, K-Banhatti and Zagreb-K-Banhatti indices. We also obtain lower and upper bounds for the Zagreb -K-Banhatti index of a graph in terms of Zagreb and K- Banhatti indices.
Graph theory, a branch of Mathematics plays a vital rule in studying interdisciplinary subjects such as physics, Chemistry, Engineering etc. Study of the properties of electrical circuits with the help of graph theory is a growing trend in mathematical and electrical fields. Electrical circuits consists of nodes and branches which obeys Kirchhoff ’s current laws, Kirchhoff ’s voltage laws etc. There are various well known theorems such as Norton’s theorem, Thevenin’s theorem, Superposition theorem, Millman Theorem etc for network analysis. In this paper, we try to analyze Millman’s theorem with the help of Graph theorem.
In thbe article, R be a ring with local units that have discussed. For any ME mod-R, the map (M1+M2):
(M1+M2)(M1+M2) given by Σn i-1/j=1 (Mi + Mj) =1 ⨂ri Σn i-1/j=1 (Mi + Mj) ⨂r be an isomorphism of right R-modules. Strongly U-Flat Modules over Matlis Domains has defined and discussed with their properties to know the relations.