Graph theory contains several topics, one of which will be discussed in this study is graph labeling. In the topic labeling, used a limited, simple, and undirected graph. study, type labeling total The multistar combination star graphs whose center vertex are not connected to each other. This research uses literature method divided into two parts, that basic calculation determine boundary first...

Let $$G = (V,E)$$ be a connected simple graph of order p and size q. A G is called local antimagic if admits labeling. bijection $$f \colon E \to \{1,2,\ldots,q\}$$ labeling for any two adjacent vertices $$u$$ $$v$$ , we have $$f^+(u) \ne f^+(v)$$ where \sum_{e\in E(u)} f(e)$$ $$E(u)$$ the set edges incident to . Thus, induces proper vertex coloring assigned color $$f^+(v)$$ The chromatic numbe...

A simple graph G = (V,E) is said to be antimagic if there exists a bijection f : E → [1, |E|] such that the addition of the values of f on edges incident to every vertex are pairwise different. The graph G = (V,E) is distance antimagic if there exists a bijection f : V → [1, |V |], such that ∀x, y ∈ V, ∑ xi∈N(x) f(xi) 6= ∑ xj∈N(y) f(xj). Using the polynomial method of Alon we prove that there a...

A graph G of order p and size q is called (a, d)-edge-antimagic total if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. The graph G is said to be super (a, d)-edge-antimagic total if the vertex labels are 1, 2, . . . , p. In this p...

Let G = (V,E) be a graph of order n. A bijection f : V → {1, 2, . . . , n} is called a distance magic labeling of G if there exists a positive integer μ such that ∑ u∈N(v) f(u) = μ for all v ∈ V, where N(v) is the open neighborhood of v. The constant μ is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. The bijection...

A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H...

Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), E(u) the set of edges incident to u. Thus, induces proper coloring G, vertex x in G assigned color ωt(x). The chromatic number, denoted by χlat(G), minimum number colors taken over al...

A graph G of order p and size q is called (a, d)-edge-antimagic total if there exists a bijection f : V(G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge-weights, w(uv) = f(u) + f (v) + f (uv), uv ∈ E(G), form an arithmetic sequence with the first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study supe...