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Published in:
2018 | OriginalPaper | Chapter
Signed Product and Total Signed Product Cordial Labeling of Cartesian Product Between Balanced Bipartite Graph and Path
Authors : Sumonta Ghosh, Anita Pal
Published in: Advanced Computational and Communication Paradigms
Publisher: Springer Singapore
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Abstract
Nowadays, signed product cordial labeling and total signed product cordial labeling play an important role in graph labeling. For the graph \(G=(V,E)\), all the vertices are label by 1 or \(-1\) with the restriction that the difference between total number of vertices labeled by 1 and \(-1\) is less than equal to 1, where edge of the graph \(G=(V,E)\) labeled by the multiplication of the label of the end vertices also with the restriction that the difference between total number of edges labeled by 1 and \(-1\) is less than equal to 1. We investigate some interesting result under the above labeling scheme on some new type of complex graph. In this paper, we apply signed product cordial labeling and total signed product cordial labeling on the graph obtained by Cartesian product between balanced bipartite graph \(K_{n,n}\) and path \(P_r\). We have shown that the time complexity of the algorithms is superlinear.