Original Research Article

Article volume = 2021 and issue = 1

Pages: 27–32

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.

##### Abstract:

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.

##### Keywords:

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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