Original Research Article
Article volume = 2021 and issue = 1
Article publication Date: February 19, 2021
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The Total Irregular Labelling of Caterpillars with Q Internal Vertices of Degree Three for All Odd Number Q > 5
M. Riski Maulana, Isnaini Rosyida, Mulyono.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang, Indonesia.
We restrict the graph G(V, E) has no loop and multiple edges, no direction on its edges, and connected. The labelling is mentioned as a “totally irregular total k-labelling” if the vertices and edges of G have different weights. The number k is said to be the total irregularity strength of G, symbolized as ts(G), if k is the minimum number such that G has “totally irregular total k-labelling”. We verify the ts of caterpillar graphs Sm,3,3, ,3,m having q internal vertices of degree 3 for odd number q > 5. The ts is: ts(Sm,3,3, ,3,m) = ceil( (2m+q-1) 2 ) for q > 5 and m > (q+5)2.
Totally irregular total k-labelling, ts, caterpillar graph, degree, internal vertex.
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Cite this article as:
- M. Riski Maulana, Isnaini Rosyida, Mulyono., The Total Irregular Labelling of Caterpillars with Q Internal Vertices of Degree Three for All Odd Number Q > 5, Communications in Combinatorics, Cryptography & Computer Science, 2021(1), PP.27–32, 2021
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