Study on the Some Labelings of Complete Bipartite Graphs
نویسندگان
چکیده
If the vertex set V of > =< V,E G can be divided into two un empty sets X and Y , ∅ = = Y V,X Y X ∩ ∪ , but also two nodes of every edge belong to X and Y separately, the G is called bipartite graph. If E ) ,y Y,(x X,y x i i i i ∈ ∈ ∈ ∀ then G is called complete bipartite graph. if n Y m, X = = , the G is marked m,n K . In this paper the graceful labeling, k-graceful labeling, odd graceful labeling and odd strongly harmonious labeling are given.
منابع مشابه
Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملConstructions of antimagic labelings for some families of regular graphs
In this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.
متن کاملVertex-Magic Total Labelings of Complete Bipartite Graphs
A vertex-magic total labeling on a graph G is a one-to-one map λ from V (G) ∪E(G) onto the integers 1, 2, · · · , |V (G) ∪E(G)| with the property that, given any vertex x, λ(x) + ∑ y∼x λ(y) = k for some constant k. In this paper we completely determine which complete bipartite graphs have vertex-magic total labelings.
متن کاملOn the cyclic decomposition of circulant graphs into bipartite graphs
It is known that if a bipartite graph G with n edges possesses any of three types of ordered labelings, then the complete graphK2nx+1 admits a cyclic G-decomposition for every positive integer x. We introduce variations of the ordered labelings and show that whenever a bipartite graph G admits one of these labelings, then there exists a cyclic G-decomposition of an infinite family of circulant ...
متن کاملVertex Magic Total Labelings of Graphs
A vertex magic total labeling of a graph with v vertices and e edges is de ned as a one to one map taking the vertices and edges onto the integers v e with the property that the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex Properties of these labelings are studied It is shown how to construct labelings for several families o...
متن کاملΓ-labelings of Complete Bipartite Graphs
Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.
متن کامل