A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

We show that rapid primordial inflation and slow asymptotic inflation is a natural consequence of Brans-Dicke theory. The ratio of the two inflation parameters is proportional to the square root of the Brans-Dicke parameter ω (ω ≫ 1). We also calculate the Hubble parameter H and the time variation of the time dependent Newtonian gravitational constant G for both regimes. The variation of the Hu...

A graceful labelling of an undirected graph G with n edges is a one-to-one function from the set of vertices of G to the set {0, 1, 2, . . . , n} such that the induced edge labels are all distinct. An induced edge label is the absolute value of the difference between the two end-vertex labels. The Graceful Tree Conjecture states that all trees have a graceful labelling. In this survey we presen...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x) o f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edge-odd gracefulness of C3  Pn and C3  2Pn is obtained. Refe...

In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C8 with some star graphs S1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C12 with some star graphs S1,r keeping two, three and five vertices gap betwee...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x) o f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edge-odd gracefulness of C3  Pn and C3  2Pn is obtained. Refe...