Global Journal of Theoretical and Applied Mathematics Sciences

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Some Results on Fibonacci Divisor Cordial Graphs


Affiliations
1 Department of Mathematics, Sri S.R.N.M. College, Sattur - 626 203, Tamil Nadu, India
2 Department of Mathematics, A.P.C. Mahalaxmi College for women, Tuticorin - 628 008, Tamil Nadu, India
3 Department of Mathematics, V.O.C. College, Tuticorin - 628 008, Tamil Nadu, India
     

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Let G = (V ,E) be a (p, q)-graph. A Fibonacci divisor cordial labeling of a graph G with vertex set V is a bijection f : V →{F1, F2, F3, . . . , Fi}, where Fi is the ith Fibonacci number such that if each edge uv is assigned the label 1 if f (u)|f (v) or f (v)|f (u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a Fibonacci divisor cordial labeling, then it is called Fibonacci divisor cordial graph. In this paper, we prove that K1,n, (n ≤ 11 and n = 10), Wn (n = 7, 8, 9 and 10) and Cm@Pn are Fibonacci divisor cordial graphs and also we prove that K1,n(n ≥ 12 and n = 10) and Wn (n = 4, 5, 6 and n ≥ 11) are not Fibonacci divisor cordial graphs.

Keywords

Cordial Labeling, Divisor Cordial Labeling, Fibonacci Divisor Cordial Labeling
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  • Some Results on Fibonacci Divisor Cordial Graphs

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Authors

R Sridevi
Department of Mathematics, Sri S.R.N.M. College, Sattur - 626 203, Tamil Nadu, India
K Palani
Department of Mathematics, A.P.C. Mahalaxmi College for women, Tuticorin - 628 008, Tamil Nadu, India
S Navanaeethakrishnan
Department of Mathematics, V.O.C. College, Tuticorin - 628 008, Tamil Nadu, India
K Nagarajan
Department of Mathematics, Sri S.R.N.M. College, Sattur - 626 203, Tamil Nadu, India

Abstract


Let G = (V ,E) be a (p, q)-graph. A Fibonacci divisor cordial labeling of a graph G with vertex set V is a bijection f : V →{F1, F2, F3, . . . , Fi}, where Fi is the ith Fibonacci number such that if each edge uv is assigned the label 1 if f (u)|f (v) or f (v)|f (u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a Fibonacci divisor cordial labeling, then it is called Fibonacci divisor cordial graph. In this paper, we prove that K1,n, (n ≤ 11 and n = 10), Wn (n = 7, 8, 9 and 10) and Cm@Pn are Fibonacci divisor cordial graphs and also we prove that K1,n(n ≥ 12 and n = 10) and Wn (n = 4, 5, 6 and n ≥ 11) are not Fibonacci divisor cordial graphs.

Keywords


Cordial Labeling, Divisor Cordial Labeling, Fibonacci Divisor Cordial Labeling

References