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Let G=(V,E) be a graph with p vertices and q edges. A graph G is said to have an even vertex odd mean labeling if there exists a function f:V(G)→{0,2,4,…,2q} satisfying f is 1-1 and the induced map f^*:E(G)→{1,3,5,…,2q-1} defined by f^* (uv)=(f(u)+f(v))/2 is a bijection. A graph that admits even vertex odd mean labeling is called an even vertex odd...
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... S.W proved the complete bipartite graph K n 1 ,n 2 has an α-valuation for all n 1 , n 2 ≥ 1 [8,3] and also its clear that if there exists an α-labeling of graph G, then G is a bipartite graph [8]. Jayanthi, Ramya and Selvi proved that the graph T @P n , T @2P n and < T o K 1,n > are even vertex odd mean graph [5]. Deligen, Lingqi Zhao, Jirimutu discussed that the k−gracefulness of r−crown I r (K m,n ) (m ≤ n, r ≥ 2) for complete bipartite graph K m,n and proved the conjecture when m = 5, for arbitrary n ≥ m and r ≥ 2 [1]. ...
A graceful labeling of a graph G(p, q) is an injective assignment of labels from the set {0, 1, ..., q} to the vertices of G such that when each edge of G has been assigned a label defined by the absolute difference of its end-vertices, the resulting edge labels are distinct. In this paper we used the new labeling technique known as M modulo N graceful labeling and prove that path union of complete bipartite graphs and join sum of complete bipartite graphs are M modulo N graceful labeling. We also give a C + + program for finding M modulo N graceful labeling on above said graphs.
... A graph G , which admits an even vertex odd mean labeling is called an even vertex odd mean graph. For more studies see [3,4]. Definition 1.2. ...
A graph G with |E(G)| = q, an injective function f : V (G) → {0, 2, 4, ..., 2q} is an even vertex odd mean labeling of G that induces the values f(u)+f(v) 2 for the q pairs of adjacent vertices u, v are distinct. In this paper, we investigate an even vertex labeling for the calendula graphs. Moreover we introduce the definition of arbitrary calendula graph and prove that the arbitrary calendula graphs are also even vertex odd mean graphs.
