The L(3; 2; 1) Labeling of Some Expanded Graphs
Let G = (V;E) be a nontrivial and connected graph. The L(3; 2; 1) labeling of graph G is a function f : V ! N [ f0g such that jf(u) ???? f(v)j 3 for every u; v 2 V with d(u; v) = 1, jf(u) ???? f(v)j 2 for every u; v 2 V with d(u; v) = 2, and jf(u) ???? f(v)j 1 for every u; v 2 V with d(u; v) =...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/42230 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G = (V;E) be a nontrivial and connected graph. The L(3; 2; 1) labeling of
graph G is a function f : V ! N [ f0g such that jf(u) ???? f(v)j 3 for every
u; v 2 V with d(u; v) = 1, jf(u) ???? f(v)j 2 for every u; v 2 V with d(u; v) = 2,
and jf(u) ???? f(v)j 1 for every u; v 2 V with d(u; v) = 3. For natural number k,
a k ???? L(3; 2; 1) labeling is an L(3; 2; 1) labeling such that no label is greater than
k. The L(3; 2; 1) number of G, denoted by 3;2;1(G) is the smallest number k such
that G has a k ???? L(3; 2; 1) labeling.
In this thesis, we give the 3;2;1 number of a book graph Bn, an expanded graph by
book graph Bm and path graph Pn, and an expanded graph by cycle graph Cm and
path graph Pn. |
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