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Divided Square Divisor Cordial and Fibonacci Prime Labeling of Theta Graphs in Python |
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PP: 149-159 |
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doi:10.18576/amis/190113
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Author(s) |
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Asokan Vasudevan,
Anto Cathrin Aanisha,
Suleiman Ibrahim Mohammad,
R. Manoharan,
N, Raja,
Osama Oqilat,
Muhammad Turki Alshurideh,
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Abstract |
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| Let Ω = (W(Ω),F(Ω)) be a graph and let h from the node set W(Ω) to set of 1, 2, ... up to total count of nodes be a one–one correspondence function. For each arc f = ab, give it a label of 1 if the absolute value of the square of h(a) minus the square of h(b), divided by the difference between h(a) and h(b) is uneven and label 0 when it is even. If the discrepancy between arcs classified 0 and 1 is no more than 1, the function h is called divided square DC labeling. Divided square DC graph has the divided square DC labeling. In this paper, we explore divided square DC labeling in the theta graph and its variations formed by merging nodes within its cycle and altering its central node and analyze its application in small social networks. Also, Fibonacci prime labeling of a graph Ω = (W (Ω ), F(Ω )) with |W (Ω )| = n is a one–to-one function h(Ω ) → { f2, f3, ..., fn+1} with fn representing the nth Fibonacci number. This labeling induces a function h∗(Ω) → N defined as h∗(cd)= maximum common divisorof h(c) and h(d), for all cd ∈ F(Ω). A graph Ω that admits a Fibonacci prime labeling is referred to as a Fibonacci prime graph. Additionally, we examine Fibonacci prime labeling in theta related graphs supported by a Python implementation.
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