Let G be a rooted product graph of path with a cycle graph with the vertex set V and the edge set E. Here n P be a Path with n vertices and m C (3) m ≥ be a cycle with a sequence of n rooted graphs m1 m2 m3 mn C ,C ,C ,-,C. We call n m P (C) the rooted product of n P by m C and it is denoted by n m P C o. Every i th vertex of n P is merging with any one vertex in every i th copy of m C. In this paper we discuss some results on rooted product graph of path with a cycle graph.

Graph theory is a fascinating subject in mathematics. Its Applications in many fields like Physical Sciences, Engineering communications, coding theory, Linguistics, Logical Algebra and Computer networking. Let G be a simple graph with vertex set V and edge set E and the function : [0,1] fV  is called a dominating function (DF) of G, if for each vV  , the sum of the function values over v and the elements incident to v is greater than or equal to one. It is a minimal dominating function (MDF), if for all gf  , g is not DF. In this paper, we study the minimal total dominating functions, minimal total roman dominating functions, minimal signed total roman dominating functions of corona product graph of a path with a complete graph and obtain total domination number () t G  , total roman domination number () tR G  and signed total roman domination number () stR G  of these graphs.

In the 21st century online marketing is the most effective wayof advertising any product or service.Online marketing helps the smallbusinesses and also startup’sin a significant manner.online marketing happens in a virtual and interactive space where the promotion of products and services takes place. The advancement in technology has drastically changed the way of marketing. In online marketing the cost-effective compared to the traditional marketing. Most of the startup’s fail due to a lack of proper strategy.Onlinemarketing is innovativelycreating a platform for start-ups in innovative manner to reach the customers the main motto of this presentation is to show the positive side of the online marketing on start-ups and small businesses.

No abstract

ABSTRACT