CORDIAL INDEX OF HONEYCOMB NETWORK GRAPH

• Main Author: SHOFY ADIANTO (10111020), ABDURRAHMAN
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20671
• Institution: Institut Teknologi Bandung

For a graph G = (V,E), a binary labeling (coloring) f : V (G)-> Z2 , is said to be friendly if the diference 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&#851; :E(G)->Z2 defined by f&#851;(xy) = |f(x)-f(y)|; Vxy € E(G). Let ef (i) = |f&#851;-1(i)| be the number of edges labeled i. The value N(f) = |ef (1)- ef (0)| is called as the cordial index for labelling f of graph G. The cordial set of the graph G, denoted by C(G), is defined by <br /> <br /> <br /> <br /> <br /> <br /> C(G) = {N(f) : f is a friendly vertex labeling of G} <br /> <br /> <br /> <br /> <br /> <br /> A graph G is said to be cordial if the value 0 or 1 is a member of C (G) <br /> <br /> <br /> <br /> <br /> <br /> A honeycomb network graph HC(n) is defined 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.