Abstract
A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of G. The degree associated reconstruction number of a graph G (or drn(G)) is the size of the smallest collection of dacards of G that uniquely determines G. It is shown that \(drn(G)=1~\text {or}~2\) for all biregular bipartite graphs with degrees d and \(d+k\), \(k\ge 2\) except the bistar \(B_{2,2}\) on 6 vertices and that \(drn(B_{2,2})=3\).
S. Monikandan—Research is supported by the SERB, Govt. of India, Grant no. EMR/2016/000157.
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The work reported here is supported by the Research Project EMR/2016/000157 awarded to the second author by SERB, Government of India, New Delhi.
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Anu, A., Monikandan, S. (2017). Degree Associated Reconstruction Number of Biregular Bipartite Graphs Whose Degrees Differ by at Least Two. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_1
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