Edge irregularity strength of uniform theta graphs, generalized 4–prism graphs, and its applications in communication networks
Umme Salma, H. M. Nagesh, U. Vijaya Chandra Kumar
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Source: Crossref
Published: Oct 23, 2025
DOI: 10.1142/s1793830925501423
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For a simple graph [Formula: see text], a vertex labeling [Formula: see text] is called a [Formula: see text]-labeling. The weight of an edge [Formula: see text] in [Formula: see text], denoted by [Formula: see text], is defined as the sum of the labels of its end vertices [Formula: see text] and [Formula: see text], i.e., [Formula: see text]. A [Formula: see text]-labeling is considered an edge-irregular [Formula: see text]-labeling if the weights of any two distinct edges are different, that is, [Formula: see text] for all pairs of distinct edges [Formula: see text] and [Formula: see text]. The smallest integer [Formula: see text] for which such an edge irregular [Formula: see text]-labeling exists is the edge irregularity strength of [Formula: see text], denoted by es[Formula: see text]. In this paper, we find the exact value for the edge irregular [Formula: see text]-labeling for uniform theta graphs [Formula: see text] for [Formula: see text] and [Formula: see text] [Formula: see text]; [Formula: see text] and [Formula: see text] [Formula: see text]; [Formula: see text] [Formula: see text], and for two classes of generalized 4-prism graphs [Formula: see text] and [Formula: see text]. Additionally, this paper discusses an application of edge irregularity strength of graphs for the optimal path selection in communication networks.
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