# Category: Issue 5

ASHWANI KUMAR GARG
Department of Education in Science and Mathematics, Regional Institute of Education, NCERT, Bhopal (M. P.), (India)
DHIRENDRA KUMAR SHUKLA
Department of Education in Science and Mathematics, Regional Institute of Education, NCERT, Bhopal (M. P.), (India)
BRAJENDRA TIWARI3
Professor, Department of Mathematics, RKDF University, Bhopal (M. P.), (India)

ABSTRACT:

In the article, R be a ring with local units that have discussed. For any ME mod-R, the map \mu(M1+M2):

(M1+M2)\rightarrow(M1+M2) given by Σn i-1/j=1 (Mi + Mj) =1 ⨂ri Σn i-1/j=1 \rightarrow(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.

KEYWORDS: U-flat modules, Matlis domains, Prufer domain

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 +...

KRISHNA GOGOI
Associate professor, D.C.B. Girlsu2019 College, Jorhat, Assam (India)
CHANDRA CHUTIA
Associate professor, Jorhat Institute of Science and Technology, Jorhat, Assam (India)

ABSTRACT:

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.

KEYWORDS: Graph theory, Electrical circuits, Branch current, Loop current

V. R. KULLI
Department of Mathematics, Gulbarga University, Gulbarga – 585 106 (India)
B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056 (India)

ABSTRACT:

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.

KEYWORDS: Zagreb index, K- Banhatti indices, Zagreb-K-Banhatti index, 2010 (AMS) Mathematics Subject Classification: 05C05, 05C07, 05C35