On super antimagic total labeling of Harary graph
نویسندگان
چکیده
This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.
منابع مشابه
On (a, d)-vertex-antimagic total labeling of Harary graphs
Let G = (V, E) be a graph with v vertices and e edges. An (a, d)-vertex-antimagic total labeling is a bijection λ from V (G) ∪ E(G) to the set of consecutive integers 1, 2, . . . , v + e, such that the weights of the vertices form an arithmetic progression with the initial term a and common difference d. If λ(V (G)) = {1, 2, . . . , v} then we call the labeling a super (a, d)-vertex-antimagic t...
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Enomoto, Llado, Nakamigawa and Ringel (1998) defined the concept of a super (a, 0)-edge-antimagic total labeling and proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In the support of this conjecture, the present paper deals with different results on super (a, d)-edge-antimagic total labeling of subdivided stars for d ∈ {0, 1, 2, 3}.
متن کاملOn super (a, d)-edge antimagic total labeling of certain families of graphs
A (p, q)-graph G is (a, d)-edge antimagic total if there exists a bijection f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2, . . . , p} and the edge labels are {p+ 1, p+ 2, . . . ,...
متن کاملOn super edge-antimagic total labeling of subdivided stars
In 1980, Enomoto et al. proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In this paper, we give a partial support for the correctness of this conjecture by formulating some super (a, d)edge-antimagic total labelings on a subclass of subdivided stars denoted by T (n, n + 1, 2n + 1, 4n + 2, n5, n6, . . . , nr) for different values of the edgeantimagic labeling...
متن کاملSuper (a, d)-edge antimagic total labelings of friendship graphs
An (a, d)-edge-antimagic total labeling of a graph G with p vertices and q edges is a bijection f from the set of all vertices and edges to the set of positive integers {1, 2, 3, . . . , p + q} such that all the edge-weights w(uv) = f(u) + f(v) + f(uv);uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edgeantimagic total labeling is called a sup...
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ورودعنوان ژورنال:
- Ars Comb.
دوره 104 شماره
صفحات -
تاریخ انتشار 2012