Let L and H be two simple, nontrivial and undirected graphs. Let o be a vertex of H, the comb product between L and H, denoted by L ▷ H, is a graph obtained by taking one copy of L and |V(L)| copies of H and grafting the ...

All graph in this paper are ¯nite, simple and connected graph. Let G(V; E) be a graph of vertex set V and edge set E. A bijection f : V (G) ¡! f1; 2; 3; :::; jV (G)jg is called a local edge antimagic labeling if for any ...

All graphs in this paper are undirected, connected and simple graph. Let G = (V,E) be a graph of order |V| and size |E|. We define a set D as a dominating set if for every vertex μ epsilon V – D is adjacent to some vertex ...

Let H be a simple and connected graph. A shackle of graph H, denoted by G = shack(H; v; n), is a graph G constructed by non-trivial graphs H such that, for every 1 · s; t · n, H have no a common vertex with js ¡ tj ¸ ...

We assume finite, simple and undirected graphs in this study. Let G, H be two graphs. By an (a,d)-H- antimagic total graph, we mean any obtained bijective function 𝑓 ∶ 𝑉 ( 𝐺 ) ∪ 𝐸 ( 𝐺 ) → {1, 2, 3, … ...

All graphs considered in this paper are finite, simple and connected graphs. Let G(V, E) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. Then a bijection f: V (G) → {1, 2, 3, ...

In this paper, we consider that all graphs are ¯nite, simple and connected. Let G(V; E) be a graph of vertex set V and edge set E. A bijection f : V (G) ¡! f1; 2; 3; :::; jV (G)jg is called a local edge antimagic labeling ...

Let G =(V (G),E(G) be a connected graph and v V (G). A dominating set for a graph G =(V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the ...

Let G be a simple, nontrivial, and connected graph. 𝑊 = {𝑤 } is a representation of an ordered set of k distinct vertices in a nontrivial connected graph G. The metric code of a vertex v, where 𝑣 ∈ G, the ordered ...

In this paper we use simple and non trivial graph. If there exist a bijective function g : V (G) [ E(G) ! f1; 2; : : : ; jV (G)j + jE(G)jg, such that for all subgraphs P 2 B H of G isomorphic to H, then graph G is ...