Abstract:
A graph G=(V,E) be a finite, simple, connected graph with |V|=p and|E|=q. An edge-antimagic total labeling is a bijective functionf:V(G)?E(G) to {1,2,…,p+q}, such that for every edge e=uv?E(G), the edge weight defined by w(e)=f(u)+f(e)+f(v) takes distinct values. If these weights form an arithmetic progression with initial term a>0 and the common difference d=0, then the labeling is called to be an (a,d)-edge antimagic total labeling. Moreover, if the labeling satisfies the condition that edge labels are 1,2,…,q, and the vertex labels are q+1,q+2,…,q+p, then it is called an e-super (a,d)-edge antimagic total labeling. This study investigates the existence and explicit construction of e-super (a,d)-EAT labeling for three graph families: path graphs? P?_n, odd cycle graphs? C?_n, where n is odd, and even cycle graphs augmented with chords and diagonals ?_nwheren=2k+2,k?N. Labeling were first derived for small instances and subsequently generalized through observed structural patterns. For each case, edge labels were assigned from 1,2, q, while vertex labels from q+1,q+2, q+p to preserve the e-super property. The research establishes bijectivity and sequential continuity without missing or repeating labels, supported by mathematical proofs in theorem form. Comparative analysis with traditional super (a,d)-EATL highlights structural differences, particularly in label assignment sequences. Potential applications include network design, cryptographic key generation, and modelling of ring topologies. Future work may extend these techniques to other graph classes, including trees, caterpillars, and related structures.
Page(s):
180-180
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
graph labeling
,
magic labeling
,
edge antimagic total labeling
,
edge weight
,
antimagic labeling