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 ...

A subset S of vertices of G is an open packing of G if the open neighborhoods of the vertices of S are pairwise disjoint in G while open packing number of G is the maximum cardinality among all the open packing sets of ...

According to the research paper on Perfect Dominating Sets by Marilynn Livingston and Quentin F. Stout[1]they have been constructed the PDSs in families of graphs arising from the interconnected networks of parallel computers ...

For the graph G = (V (G), E(G)), a function f : V (G) → {0, 1} is called a product cordial labeling of G if the induced edge labeling function defined by the product of end vertex labels be such that the edges with label ...

A dominating set S ⊆ V (G)of a graph G is called restrained dominating set if every vertex in V (G) - S is adjacent to a vertex in S and to a vertex in V (G) - S. The restrained domination number of G, denoted by γ_r (G), ...

Domination theory is a part of Graph theory is used for finding communities in networks, device for modeling, description of real world network systems such are : Transport, Water, Electricity, Internet and many more. ...

A function f: V(G) →{2,4, …, 2|E(G)|} is called an even mean labeling of graph G if it is injective and when each edge e=uv is labeled with average sum of f(u) and f(v) then the resulting edge labels are distinct. Here ...

A vertex dominating set D of V (G) is called a chromatic transversal dominating set of G if D intersects every color class of G. The minimum cardinality of D is called a chromatic transversal domination number of G. In ...

The eigenvalue of a graph G is the eigenvalue of its adjacency matrix. The energy E (G) of G is the sum of absolute values of its eigenvalues. A natural question arises: How the energy of a given graph G can be related ...

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the litera- ture, in which the energy is de_ned for the Laplacian ...