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...

[Puget, 2004] has shown that if the symmetry in a constraint satisfaction problem acts only on the variables and there is also an allDifferent constraint on the variables, the symmetry can be eliminated by adding a small number of constraints, linear in the number of variables. In this paper, Puget’s procedure for finding a set of symmetrybreaking constraints is extended to find all possible di...

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...

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...

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...

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...

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...

A tree of order n is said to be graceful if the vertices can be assigned the labels {0, . . . , n−1} such that the absolute value of the differences in vertex labels between adjacent vertices generate the set {1, . . . , n− 1}. The Graceful Tree Conjecture is the unproven claim that all trees are graceful. We present major results known on graceful trees from those dating from the problem’s ori...