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We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in physics. We also analyze a variant of these polynomials for colored embedded graphs. This is used to describe the change in the polynomial under basic graph theoretic operations. We conclude with several applications of this polynomial including detection of certain classes of graphs and the connection of this polynomial with topological entanglement entropy.

Gone are those days when having a cabled phone was a very big thing, but nowadays, mobile phones have become a basic necessity of life. Technology has grown exponentially in past few decades in every dimension of life. Did anybody ever wonder that one day they would have a small computer on their wrist? A computer that will guide them, assist them in their day to day activities.It is now possible in the form of a small computerized watch called the Smart Watch, a kind of wearable technology which assists them in day-to-day tasks and also monitors their fitness. General TermsWearable technology is such which can be worn and performs smart applications like tracking health related information, sync the information with the database etc.Smart Watch is a mobile device which comes under wearable technology and keeps people updated about their day-to-day task without them checking their Smartphone every time.

Given a Union-Closed family, which is not equal to the power set of its universe, say [n], one can always add a new set A[n] to it, such that the new family remains Union-Closed. We construct a new family by collecting all such A's and call this family the closure of F. We study various properties of this closure. We characterize families whose closure becomes the power set of [n] and give a checking criteria of closure roots of such families, i.e., existence of H such that closure of H = F.