Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph - P. Anusha Devi; S. Monikandan (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2015)
An ecard of a graph G is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph G, dern(G), is the minimum number of da-ecards that uniquely determines G. The adversary degree associated edge reconstruction number of a graph G, adern(G), is the minimum number k such that every collection of k da-ecards of G uniquely determines G. The maximal subgraph without end vertices of a graph G which is not a tree is the pruned graph of G. It is shown that dern of complete multipartite graphs and some connected graphs with regular pruned graph is 1 or 2. We also determine dern and adern of corona product of standard graphs.