ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
A total vertex irregular k-labelling on graph G is dened as a mapping, : V (G) [ E(G) ????! f1; 2; : : : ; kg, in which for every distinct two vertices x; y 2 V (G), we have wt(x) 6= wt(y). The minimum k in which G has a total vertex irregular k-labelling dened as total vertex irregularity stren...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/47697 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A total vertex irregular k-labelling on graph G is dened as a mapping,
: V (G) [ E(G) ????! f1; 2; : : : ; kg, in which for every distinct two vertices
x; y 2 V (G), we have wt(x) 6= wt(y). The minimum k in which G has a
total vertex irregular k-labelling dened as total vertex irregularity strength of
graph G, denoted tvs(G).
Let G1 and G2 be any graph. A Cartesian product of graph G1 and G2, deno-
ted by G1G2, is the graph with the set of vertices V (G1G2) = f(ui; vj)jui 2
V1; vj 2 V2g and the set of edges E(G1G2) = f(ui; vj)(uk; vl)jui = uk dan vjvl 2
E2, or vj = vl and uiuk 2 E1g.
In this research, we build an algorithm to determine the total vertex irregula-
rity strength of cartesian product of Pn Cm for m; n 3. As the results of
this research, we obtained
tvs(Pn Cm) =
3 + mn
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