Punjab University Journal of Mathematics, Vol 50, No 3 (2018)

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SEMT Valuations of Disjoint Union of Combs, Stars and Banana Trees

Salma Kanwal, Isma Kanwal


A Graph G = (V (G), E(G)) is the set of points called vertices or(nodes) and the lines connecting these points are called edges. The number of vertices in a graph is called its order and the number of edges is called its size, usually denoted as |V (G)| = n (or p) and |E(G)| = m ( or q) respectively. A graph G with p nodes and q lines admits the edge magic total labeling if there exists a one-one, onto map ψ : V (G) ∪ E(G) → {1, p + q} = {1, 2, 3, . . . , p + q} s.t weight of every edge is some same constant (say )k, such number k is called the magic constant. If a graph G has an edge magic total labeling ψ : V (G) → {1, 2, 3, . . . , p} then ψ is called super edge magic total( SEMT) labeling. For graph G, SEMD is the number of isolated vertices whose union with G makes the resulting graph SEMT. µs(G), is the minimum non-negative integer n such that G ∪ nK1 SEMD will be +∞ if no isolated vertex do this job. In this work SEMT labeling and deficiencies are determined for forests formed by two sided generalized combs, stars, combs and banana trees

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