On (almost) 2-Y-homogeneous distance-biregular graphs

Let $$\Gamma $$ denote a bipartite graph with vertex set X and color partitions Y, $$Y'$$ . For nonnegative integer i $$x\in X$$ , let _{i}(x)$$ the of vertices in that are at distance from x. Y$$ $$y \in \Gamma _2(x)$$ $$z _{i}(x)\cap _i(y)$$ $$\gamma _i(x,y,z)$$ number common neighbors x y which $$i-1$$ z (i.e., _i(x,y,z):=|\Gamma _1(x)\cap _{1}(y)\cap _{i-1}(z)|$$ ). moment assume every Y has eccentricity $$D\ge 3$$ Graph is almost 2-Y-homogeneous whenever for all $$i \; (1\le \le D-2)$$ independent choice x, z. In addition, if above condition holds also $$i=D-1$$ then we say 2-Y-homogeneous. this paper, study combinatorial structure distance-biregular graphs. We give sufficient necessary conditions under (almost) Moreover, write intersection numbers class terms three parameters.