A binary vertex labeling f : E(G) → {0, 1} with induced labeling f ∗ : V (G) → {0, 1} defined by f ∗ P (v) = {f(uv) | uv ∈ E(G)}(mod 2) is called E-cordial labeling of a graph G if the number of vertices labeled 0 ...

A graph with q edges is called antimagic if its edges can be labeled with 1, 2,…,q such that the sums of the labels of the edges incident to each vertex are distinct. Here we prove that the graphs obtained by switching ...

We investigate E-cordial labeling for some cartesian product of graphs. We prove that the graphs Kn × P2 and Pn × P2 are E-cordial for n even while Wn × P2 and K1,n × P2 are E-cordial for n odd.

For a graph G=(V, E), a set S⊆ V (S⊆ E) is a restrained dominating (restrained edge dominating) set if every vertex (edge) not in S is adjacent (incident) to a vertex (edge) in S and to a vertex (edge) in V-S (ES). The ...

For a graph G = (V,E), a subset D of E is restrained edge dominating set of G if every edge not in D is adjacent to an edge in D as well as an edge in E −D. The restrained edge domination number of G, denoted by γre(G) is ...

For a graph G = (V, E), a set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V − S. The smallest cardinality of a restrained dominating set of G is called ...

We determine the energy of a graph obtained by means of graph operations on a given graph, and relate the energy of such a new graph with that of the given graph.

If G is a graph with vertex set V (G) then dominating set D⊆ V (G) is called total if every vertex of V (G) is adjacent to at least one vertex of D while it is called equitable if for every vertex u in V (G)− D there exists ...

If for any total dominating set D with ν ∈ V (G) − D there exists a vertex u ∈ D such that uν ∈ E (G) and |d(ν)−d(u)| ≤ 1 then D is called the total equitable dominating set. The minimum cardinality of the total equitable ...

A proper k - coloring of a graph G is a function f : V(G) → {1,2,..., k} such that f(u) 6= f(v) for all uv ∈ E(G). The color class Si is the subset of vertices of G that is assigned to color i. The chromatic number χ(G) ...