For a connected graph of order n, the metric basis of a G is a smallest set {} k v vv S,,, 2 =1 of vertices of G such that for vertex, G u∈ the ordered k-tuples of are all distinct.distances {()()()()} k vud vud vud ...

The eigenvalue of a graph G is the eigenvalue of its adjacency matrix and the energy E(G) is the sum of absolute values of eigenvalues of graph G. Two non-isomorphic graphs G1 and G2 of the same order are said to be ...

In year 2013, L. Thivagar et al. introduced nano topological space and he analysed some properties of weak open sets. In this paper we shall introduce Kasaj-topological space. We shall introduce some new classes of weak ...

A radio labeling of a graph $G$ is a function $f$ from the set of vertices $V(G)$ to the set of non-negative integers such that $|f(u)-f(v)|\geq \diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$. 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 ...

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), ...