On total edge irregularity strength of tadpole chain graph Tr(6, n)

Given a graph G(V, E) with a non-empty set of vertices V and a setof edges E. A total labelling f: V ∪ E → {1,2,..., k} is called an edge irregular total labeling if the weight of every edge is distinct. The weight of anedgee, under the total labeling f, is the sum of label of edgee and all labels o...

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Bibliographic Details
Published in:Journal of physics. Conference series 2020-05, Vol.1538 (1), p.12001
Main Authors: Nurdini, E, Rosyida, I, Mulyono
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Chains
Graph theory
Irregularities
Labeling
Labels
Weight
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Summary:Given a graph G(V, E) with a non-empty set of vertices V and a setof edges E. A total labelling f: V ∪ E → {1,2,..., k} is called an edge irregular total labeling if the weight of every edge is distinct. The weight of anedgee, under the total labeling f, is the sum of label of edgee and all labels of vertices that are incident to e. In other words, wt(xy) = f(xy) + f(x) + f(y). The total edge irregularity strength of G, denoted by tes(G) is the minimum k used to label graph G with the edge irregular total labeling. A tadpole chain graph of length r, denoted as Tr (6, n), is a chain graph that consists of tadpole graph T (6, n) on each block. In this paper, we get tes(Tr(6,n))=⌈ (6+n)r+23 ⌉ and construct an algorithm to find it.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1538/1/012001