The total disjoint irregularity strength of some certain graphs

Meilin I Tilukay, A. N. M. Salman

Abstract


Under a totally irregular total k-labeling of a graph G = (V, E), we found that for some certain graphs, the edge-weight set W (E) and the vertex-weight set W (V ) of G which are induced by k=ts(G), W(E)∩W(V) is a non empty set. For which k, a graph G has a totally irregular total labeling if W (E) ∩ W (V ) = ∅? We introduce the total disjoint irregularity strength, denoted by ds(G), as the minimum value k where this condition satisfied. We provide the lower bound of ds(G) and determine the total disjoint irregularity strength of cycles, paths, stars, and complete graphs.


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DOI: http://dx.doi.org/10.19184/ijc.2020.4.2.2

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