L(2,1) LABELING OF COMB PRODUCT OF STAR, PATH, AND COMPLETE GRAPH
Let G = (V,E) be a simple graph. An L(2, 1)?labeling of G is a whole number valued function f : V (G) ? N0 such that, whenever u and v are two adjacent vertices in V, then |f(u) ? f(v)| ? 2 if d(u, v) = 1 and |f(u) ? f(v)| ? 1 if d(u, v) = 2. The labeling number L(2, 1) of G, denoted by ?2,1(G),...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/73301 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G = (V,E) be a simple graph. An L(2, 1)?labeling of G is a whole number
valued function f : V (G) ? N0 such that, whenever u and v are two adjacent
vertices in V, then |f(u) ? f(v)| ? 2 if d(u, v) = 1 and |f(u) ? f(v)| ? 1 if
d(u, v) = 2. The labeling number L(2, 1) of G, denoted by ?2,1(G), is the smallest
number m so that G has labeling L(2, 1) with no more labels greater than m. In
this thesis, will further discuss the L(2, 1) labeling of graph of comb product of
star, path, and complete graph. The purpose of this research is to determine the
minimum span value of ?2,1(G ?o H) on the graph of comb product of star graph
(?2,1(G ?o K1,n)), the graph of comb product of path graph (?2,1(G ?o Pn)), and
the graph of comb product of complete graph (?2,1(G ?o Kn)). |
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