Malaysian Journal of Mathematical Sciences, January 2021, Vol. 15, No. 1
Edge Irregular \(k\)-labeling for Disjoint Union of Cycles and Generalized Prisms
Hasni, R., Tarawneh, I., Siddiqui, M. K., Raheem, A., and Asim, M. A.
Corresponding Email: hroslan@umt.edu.my
Received date: 22 January 2020
Accepted date: 29 November 2020
Abstract:
For a simple graph \(G\), a vertex labeling \(\phi :V(G)\rightarrow \left \{ 1,2,...,k \right \}\) is called \(k\)-labeling. The weight of an edge \(xy\) in \(G\), denoted by \(w_{\pi}(xy)\), is the sum of the labels of end vertices \(x\) and \(y\), i.e. \(w_{\phi}(xy)=\phi(x)+\phi(y)\). A vertex \(k\)-labeling is defined to be an edge irregular \(k\)-labeling of the graph \(G\) if for every two different edges \(e\) and \(f\), there is \(w_{\phi}(e)\neq w_{\phi}(f)\). The minimum
\(k\) for which the graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\), denoted by \(es(G)\). In this paper, we
determine the exact value of edge irregularity strength of disjoint union of cycles and generalized prisms. These results proved the upper bound
for edge irregularity strength for such graphs and can be used in future for addressing schemes in different applications.
Keywords: Irregular assignment, edge irregularity strength, disjoint union, cycle, generalized prism
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