Tanner graphs which represented low density parity check (LDPC) codes have 20 become an interesting research topic. Finding the number of short cycles of Tanner 21 graphs motivated Blake and Lin to investigate the multiplicity of cycles of length equal 22 to the girth of bi-regular bipartite graphs by using the spectrum and degree distribution 23 of the graph. While there were many algorithms to find the number of cycles, they chose 24 to take a computational approach. Dehghan and Banihashemi counted the number of 25 cycles of length g + 2 and g + 4, where G is a bi-regular bipartite graph and g is the 26 girth of G. But for the cycles of length smaller than 2g in bi-regular bipartite graphs, 27 they only proposed a descriptive technique. In this paper, we find the number of cycles 28 of length less than 2g by using the spectrum and the degree distribution of bi-regular 29 bipartite graphs such that the formula depends only on the partitions of positive integers 30 and the number of closed cycle-free walks from any vertex of Bc,d and Tc,d, which are 31 known.

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