Cyclic-coverings of Line graph $L(S_n)$ and its Disjoint Union
Volume 2 (2023) Issue 1,
DOI:
https://doi.org/ 10.71448/jcm2023v2i13
Submission Received: 23 Jan 2023
Revised: 22 May 2023
Accepted: 05 Jun 2023
Published: 30 Jun 2023
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Abstract
A graph is a particular representation of a static network and labeling of a graph can be think of as automatic routing of data in a network topology.
A visual representation of data in the form of a graph help us to look deep insight. The data science (e.g., Python Package: a computer programming language) uses graph theory concepts to study and analyze the networks. Analyzing these network is equivalent of finding a set of edges $E'$ for a graph $G$ such that every vertex of $G$ is incident with at least one edge in $E'$. Then $E'$ is called an {\it edge-covering} of $G$. A spanning tree of a connected graph is an example of edge-covering. A finite simple graph $G$ is an $(a_d,d)$-$H$-antimagic if the following three conditions are satisfied: $G$ has an $H$-covering ($H$ a subgraph of $G$), there exists a bijection $\alpha: V(G)\cup E(G)\rightarrow \{1,2,3,\dots,|V(G)\cup E(G)|\}$ and the $H$-weights constitute an arithmetic progression with common difference $d$. The above said labeling is called super if ${\alpha}(V)=\{1,2,\dots,|V|\}$. In this research article, we focused on studying super $C_3$-antimagic labeling of line graph of a sun-let graph for several differences and $C_3$-supermagic labeling of its disjoint union.
Keywords
Network representation,$C_3$-coverings,star graph,sun-let graph,line graph,disjoint union of graphs