Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications

Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph

P. Anusha Devi (Department of Mathematics Manonmaniam Sundaranar University Tirunelveli -- 627 012 Tamilnadu INDIA)
S. Monikandan (Department of Mathematics Manonmaniam Sundaranar University Tirunelveli -- 627 012 Tamilnadu INDIA)



Article Info

Publish Date
07 Oct 2015

Abstract

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.

Copyrights © 2015






Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...