Computing Edge Weights of Symmetric Classes of Networks

Abstract

Accessibility, robustness, and connectivity are the salient structural properties of networks. The labelling of networks with numeric numbers using the parameters of edge or vertex weights plays an eminent role in the study of the aforesaid properties. The systems interlinked in a network are transformed into a graphical network, and specific numeric labels assigned to the converted network under certain rules assist us in the regulation of data traffic, bandwidth, and coding/decoding of signals. Two major classes of such network labellings are magic and antimagic. The notion of super $\left(a,0\right)$ edge-antimagic labelling on networks was identified in the late nineties. The present article addresses super $\left(a,0\right)$ edge antimagicness of union of the networks’ star $S_n$ , the path $P_n$ , and copies of paths and the rooted product of cycle $C_n$ with $K_{2,m}$ . We also provide super $\left(a,0\right)$ edge-antimagic labelling of the rooted product of cycle $C_n$ and planar pancyclic networks. Further, we design a super $\left(a,0\right)$ edge-antimagic labelling on a pancyclic network containing chains of $C_6$ and three different symmetrically designed lattices. Moreover, our findings have also been recapitulated in the shape of 3- $D$ plots and tables.