@article{Article_5,

title = {The Total Irregular Labelling of Caterpillars with Q Internal Vertices of Degree Three for All Odd Number Q > 5},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2021},

issue = {1},

issn = { 2783-5456 },

year = {2021},

url = {http://cccs.sgh.ac.ir/Articles/2021/issue 1/1-5-the_total_irregular_labelling_of_caterpillars_with_q_internal_vertices_of_degree_three_for_all_odd_number_q__5-1636016220.pdf},

author = {M. Riski Maulana and Isnaini Rosyida and Mulyono.},

keywords = {Totally irregular total k-labelling, ts, caterpillar graph, degree, internal vertex.},

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.}

};