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2021 | 155 | 98-112
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Pentagonal Graceful Labeling of Some Graphs

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Numbers of the form (n(3n-1))/2 for all n ≥ 1 are called pentagonal numbers. Let G be a graph with p vertices and q edges. Let f : V(G)→{0,1,2,…,P_q} where P_q is the q^th pentagonal number be an injective function. Define the function f *: E(G) → {1,5,…,P_q} such that f *(uv)=│f(u)-f(v)│for all edges uv∈E(G). If f *( E(G)) is a sequence of distinct consecutive pentagonal numbers {P_1,P_2,…,P_q}, then the function f is said to be pentagonal graceful labeling and the graph which admits such a labeling is called a pentagonal graceful graph. In this paper, pentagonal graceful labeling of some graphs is studied.
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  • Department of Mathematics, The Madurai Diraviyam Thayumanavar Hindu College, Tirunelveli, India
  • Department of Mathematics, The Madurai Diraviyam Thayumanavar Hindu College, Tirunelveli, India
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