Further Results on Super (a, d) Edge-Antimagic Graceful Labeling of Graphs

An (a, d)-edge-antimagic graceful labeling is a bijection g from V(G) ∪ E(G) into {1,2, ..., |V(G)| + |E(G)|} such that for each edge xy ∈ E(G), |g(x) + g(y) - g(xy) form an arithmetic progression starting from a and having a common difference d. An (a, d)edge-antimagic graceful labeling is called s...

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Bibliographic Details
Published in:International journal of mathematical combinatorics 2023-12, Vol.4, p.75-81
Main Author: Krishnaveni, P
Format: Article
Language:English
Subjects:
Graphs
Labeling
Online Access:Get full text
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Summary:An (a, d)-edge-antimagic graceful labeling is a bijection g from V(G) ∪ E(G) into {1,2, ..., |V(G)| + |E(G)|} such that for each edge xy ∈ E(G), |g(x) + g(y) - g(xy) form an arithmetic progression starting from a and having a common difference d. An (a, d)edge-antimagic graceful labeling is called super (a, d)-edge-antimagic graceful if g(V(G)) = {1,2, ...,|V(G)|}. A graph that admits an super (a, d)-edge-antimagic graceful labeling is called a super (a, d)-edge-antimagic graceful graph. In this paper, we prove the super (a, d) edge antimagic gracefulness of regular graphs. Later, we study the non-regular graph is super (a, 1)-edge-antimagic graceful graph. Finally, we find super edge-antimagic graceful labeling of some classes of graphs.
ISSN:1937-1055
1937-1047