MODULAR IRREGULAR LABELING OF DOUBLE BROOM GRAPH
Let G = (V, E) be a graph of order n with nonempty vertex set V and edge set E. Let t be a positive integer. A modular irregular labeling of graph G is an edge t-labeling ? : E ? [1, t] such that there exists a bijective weight function wt? : V ? Zn, where Zn be a group of modulo n. The modular w...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/81489 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G = (V, E) be a graph of order n with nonempty vertex set V and edge set
E. Let t be a positive integer. A modular irregular labeling of graph G is an
edge t-labeling ? : E ? [1, t] such that there exists a bijective weight function
wt? : V ? Zn, where Zn be a group of modulo n. The modular weight function
of vertex u defined by wt?(u) =
P
v?N(u) ?(uv). Furthermore, ms(G) denote the
modular irregularity strength of graph G that is the minimum number t such that a
graph G has modular irregular labeling with largest label t. Let k, l be a positive
integer. The double broom which denoted by DBk,l is a graph of order k + 2l which
obtained by identifying each pendant vertices z1 and zk of path graph of order k with
center vertex of each star graph of order l + 1. In this research, we construct the
modular irregular labeling for double broom graph and determine the exact value
of the modular irregularity strength for large enough k + 2l. |
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