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Sum divisor cordial labeling for path and cycle related graphs. (English) Zbl 1448.05175

Summary: A sum divisor cordial labeling of a graph \(G\) with vertex set \(V\) is a bijection \(f\) from \(V\) to \(\{1, 2, \cdots, |V(G)|\}\) such that an edge \(uv\) is assigned the label 1 if 2 divides \(f(u) + f(v)\) and \(0\) otherwise; and the number of edges labeled with \(0\) and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that \(P^2_n, P_n \odot mK_1, S(P_n \odot mK_1), D_2(P_n), T(P_n)\), the graph obtained by duplication of each vertex of path by an edge, \(T(C_n), D_2(C_n)\), the graph obtained by duplication of each vertex of cycle by an edge, \(C^{(t)}_4\), book, quadrilateral snake and alternate triangular snake are sum divisor cordial graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)

References:

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