CORDIAL INDEX OF HONEYCOMB NETWORK GRAPH
For a graph G = (V;E), a binary labeling (coloring) f : V (G) ! Z2 , is said to be friendly if the dierence between the number of vertices labeled 0 and vertices labeled 1 is at most 1. The friendly labeling f : V (G) ! Z2 induces an edge labeling f : E(G) ! Z2 dened by f(xy) = jf(x)????f(y)j; 8x...
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| Format: | Final Project |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/33859 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | For a graph G = (V;E), a binary labeling (coloring) f : V (G) ! Z2 , is said to
be friendly if the dierence between the number of vertices labeled 0 and vertices
labeled 1 is at most 1. The friendly labeling f : V (G) ! Z2 induces an edge labeling
f : E(G) ! Z2 dened by f(xy) = jf(x)????f(y)j; 8xy 2 E(G). Let ef (i) = jf????1
(i)j
be the number of edges labeled i. The value N(f) = jef (1) ???? ef (0)j is called as the
cordial index for labelling f of graph G. The cordial set of the graph G, denoted by
C(G), is dened by
C(G) = fN(f) : f is a friendly vertex labeling of Gg:
A graph G is said to be cordial if the value 0 or 1 is a member of C(G).
A honeycomb network graph HC(n) is dened as follows: HC(1) is a hexagon. For
n > 1, HC(n) is obtained from HC(n ???? 1) by adding a layer of hexagons around
the boundary of HC(n ???? 1). In this thesis, we show that HC(n) with n > 1 is a
cordial graph. We also characterize all values of cordial index of HC(n) for n > 1. |
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