Vertex-magic total labelings of disconnected graphs. | [Journal of Prime Research in Mathematics • 2006]

Author(s):

1. Slamin: Mathematics Education Study Program, FKIP, Universitas Jember, Jalan Kalimantan 37 Jember 68121 Indonesia

2. A. C. Prihandoko: Mathematics Education Study Program, FKIP, Universitas Jember, Jalan Kalimantan 37 Jember 68121 Indonesia

3. T. B. Setiawan: Mathematics Education Study Program, FKIP, Universitas Jember, Jalan Kalimantan 37 Jember 68121 Indonesia

4. F. Rosita: Mathematics Education Study Program, FKIP, Universitas Jember, Jalan Kalimantan 37 Jember 68121 Indonesia

5. B. Shaleh: School of Mathematical Sciences, GC University, 68-B New Muslim Town, Lahore, Pakistan

6. Slamin: School of Mathematical Sciences, GC University, 68-B New Muslim Town, Lahore, Pakistan

Abstract:

Let G be a graph with vertex set V = V(G) and edge set E = E(G) and let e = ÷E(G)÷. A one-to-one map l from V U E onto the integers {1,2,…,u + e} is called vertex magic total labeling if there is a constant k so that for every vertex x, l(x) + ∑ l(xy) = k where the sum is over all vertices y adjacent to x. Let us call the sum of labels at vertex x the weight wl(x) of the vertex under labeling l; we require wl(x) = k for all x. the constant k is called the magic constant for l. In this paper, we present the vertex magic total labelings of disconnected graph, in particular, two copies of isomorphic generalized Petersen graphs 2P(n,m), disjoint union of two non-isomorphic suns Sm U Sn and t copies of isomorphic suns tSn.

Page(s): 147-156

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 2, Issue: 0, Year: 2006

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