ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM

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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Main Author: Tumpi Nagari, Grita
Format: Theses
Language:Indonesia
Online Access:https://digilib.itb.ac.id/gdl/view/47697
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Institution: Institut Teknologi Bandung
Language: Indonesia
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spelling id-itb.:476972020-06-17T16:40:47ZON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM Tumpi Nagari, Grita Indonesia Theses 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 5 : INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/47697 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 5 : text
institution Institut Teknologi Bandung
building Institut Teknologi Bandung Library
continent Asia
country Indonesia
Indonesia
content_provider Institut Teknologi Bandung
collection Digital ITB
language Indonesia
description 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 5 :
format Theses
author Tumpi Nagari, Grita
spellingShingle Tumpi Nagari, Grita
ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
author_facet Tumpi Nagari, Grita
author_sort Tumpi Nagari, Grita
title ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
title_short ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
title_full ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
title_fullStr ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
title_full_unstemmed ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF CARTESIAN PRODUCT GRAPH OF PN AND CM
title_sort on the total vertex irregularity strength of cartesian product graph of pn and cm
url https://digilib.itb.ac.id/gdl/view/47697
_version_ 1822927729880727552

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