New class of integral bipartite graphs with large diameter

Document Type : Research Paper


Shahed university, Tehran, Iran.


In this paper‎, ‎we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters‎. ‎In fact‎, ‎for every finite set $A$ of positive integers of size $k$ we construct an integral bipartite graph $G$ of diameter $2k$ such that the set of positive eigenvalues of $G$ is exactly $A$‎. ‎This class of integral bipartite graphs has never found before‎.


Main Subjects

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  • Receive Date: 04 February 2016
  • Revise Date: 26 September 2016
  • Accept Date: 01 October 2016
  • Published Online: 01 March 2018