Let N0 denote the set of all non-negative integers and X be any subset of X. Also denote the power set of X by P(X). An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) ! P(X) such that the induced function f+ : E(G) ! P(X) is defined by f+(uv) = f(u) + f(v), where f(u) + f(v) is the sumset of f(u) and f(v). An IASL f is said to be a topological IASL (Top-IAS...

<p>Among the most studied graph labelings we have varieties called alpha and edge-magic. Even when their definitions seem completely different, these are related. A graceful labeling of a bipartite is an α-labeling if smaller labels assigned to vertices same stable set. An edge-magic size <em>n</em> said be <em>b</em>-edge consecutive its edges labeled with integer...

We establish that all trees on at most 27 vertices admit graceful labellings and all trees on at most 26 vertices admit harmonious labellings. A graceful labelling of a graph G with q edges is an injection f : V (G) → {0, 1, 2, . . . , q} such that when each edge xy ∈ E(G) is assigned the label, |f(x) − f(y)|, all of the edge labels are distinct. A graph which admits a graceful labelling is sai...

For a defined graph labeling, there exists a number of bijective functions for a graph of defined order and size which leads to different graphs. In this paper, a mathematical tool is developed to find the number of super vertex graceful graphs for a defined order “p” and size “q”. Mathematics Subject Classification: 05C78

Symmetry in a Constraint Satisfaction Problem can cause wasted search, which can be avoided by adding constraints to the CSP to exclude symmetric assignments or by modifying the search algorithm so that search never visits assignments symmetric to those already considered. One such approach is SBDS (Symmetry Breaking During Search); a modification is GAP-SBDS, which works with the symmetry grou...

We conjecture that any 2-regular simple graph has an SSA labeling. We provide several special cases to support our conjecture. Most of our constructions are based on Skolem sequences and on an extension of it. We establish a connection between simply sequentially additive labelings of 2-regular graphs and ordered graceful labelings of spiders.

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...

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...