Abstract:
This paper examines ?????????? (??, ??) − ?????????? ?? − ???????? (??1,3)-anti-magic labeling for the family of flower snark graphs ???? with ?? ≥ 3. A total labeling is defined as a bijection from (????) (????) onto{1,2, . , |??(????)| + |??(????)|}, while the super condition requires that vertices receive the smallest possible labels. A labeling is called (??, ??)− ?????????? ?? − ???????? ???????? − ?????????? if, for all subgraphs of ???? isomorphic to Y-Star, the total weights-obtained by summing the labels of the vertices and edges in the subgraph-form an arithmetic progression with first terma and common difference d ≥ 0. We provide explicit constructions of such labeling for all n≥3 establishing that flower snark graphs admit super (a,d)- total Y star K1,3 -anti-magic labeling for a broad range of d values. The case d = 1 yields consecutive integer weights, while other values of d produce evenly spaced sequences of total weights. A further contribution of this work is the investigation of the prime arithmetic progression case, where all terms in the weight sequence are prime numbers. This condition is highly restrictive, yet wedemonstrate its feasibility for various instances within the flower snark family. The labeling techniques introduced are constructive and adaptable, extending naturally to other cubic snark graphs such as the generalized Jahangir graphs J2k+1, The results presented contribute new infinite families of graphs possessing both general and prime AP super (a,d)-total Y-star K1,3 -anti-magic labelings, thereby enriching the study of anti-magic labelings in cubic and snark graph classes.
Page(s):
179-179
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:
Super a
,
arithmetic progression
,
dtotal Y star K1
,
prime arithmatic progression
,
flower snark graph
,
3 antimagic labeling