Abstract
Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering. For example, in network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain rules help us in the regulation of data traffic, connectivity, and bandwidth as well as in coding/decoding of signals. Especially, both antimagic and magic graphs serve as models for surveillance or security systems in urban planning. In 1998, Enomoto et al. introduced the notion of super a,0 edge-antimagic labeling of graphs. In this article, we shall compute super a,0 edge-antimagic labeling of the rooted product of Pn and the complete bipartite graph K2,m combined with the union of path, copies of paths, and the star. We shall also compute a super a,0 edge-antimagic labeling of rooted product of Pn with a special type of pancyclic graphs. The labeling provided here will also serve as super a′,2 edge-antimagic labeling of the aforesaid graphs. All the structures discussed in this article are planar. Moreover, our findings have also been illustrated with examples and summarized in the form of a table and 3D plots.
Highlights
Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering
In network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain rules help us in the regulation of data traffic, connectivity, and bandwidth as well as in coding/decoding of signals
We shall compute a super (a, 0) edgeantimagic labeling of rooted product of Pn with a special type of pancyclic graphs. e labeling provided here will serve as super (a′, 2) edge-antimagic labeling of the aforesaid graphs
Summary
E main reason for this unwanted interruption is constraint-free transmission of the concurrent networks admitting same instance appearance [8, 9] Such networks are first converted into graphs and magic labeling helps in assigning constant weights to the concurrent networks. The radio labeling of graphs is tremendously helpful in the minimization of the problem of interference in wireless networks and has been playing a very vital role in the last few years. E challenge for base cell here is to provide maximum channel reuse without violating the constraints in order to minimize the blocking To tackle this challenge, a label is assigned to each user and the communication link of this user receives a distinct label.
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