For positive integers $m_1,m_2,\dots ,m_h$, a generalized balanced tree $T(m_1,m_2,\dots ,m_h)$ is a rooted tree of height h such that every vertex of depth i has $m_{i+1}$ children, $0\le i\le h-1$. The distance matrix $D(G)$ of a simple connected graph G of order n is an $n\times n$ matrix whose $(i,j)\mathrm{th}$ entry is the distance between $i\mathrm{th}$ and $j\mathrm{th}$ vertices. A connected graph G is called a k-partitioned transmission regular graph if there exists a vertex partition $\{V_1,V_2,\dots ,V_k\}$ of G so that for $1\le i,j\le k$, and $x\in V_i$, $\sum _{y\in V_j}d(x,y)$ is a constant. Here we show that $T(m_1,m_2,\dots ,m_h)$ is an $(h+1)$-partitioned transmission regular graph. We find an $(h+1)\times (h+1)$ matrix whose largest eigenvalue is the distance spectral radius of $T(m_1,m_2,\dots ,m_h)$. We obtain the characteristic polynomial of $D(T(m_1,m_2,\dots ,m_h))$ in terms of that of the smaller matrices and give an idea to find the full spectrum. Moreover, we get that $D(T(m_1,m_2,\dots ,m_h))$ has $-2$ an eigenvalue with multiplicity at least $m_1\cdots m_{h-1}(m_h-1)$ and $-(m_h+2)\pm \sqrt{m_h(m_h+4)}$ as eigenvalues with multiplicity at least $m_1\cdots m_{h-2}(m_{h-1}-1)$.

对于正整数${米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H$, 一棵广义平衡树$吨({米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H)$是一棵高度为h的有根树，深度为i的每个顶点都有${米}_{我+\mathrm{1个}}$孩子们，$0\le 我\le H-\mathrm{1个}$. 距离矩阵$丁(G)$一个n阶的简单连通图G是一个$n\times n$矩阵其$(我,j)\mathrm{日}$输入是之间的距离$我\mathrm{日}$和$j\mathrm{日}$顶点。如果存在顶点划分，则连通图G称为k划分传输正则图$\{V_{\mathrm{1个}},V_{\mathrm{2个}},\dots \dots ,V_k\}$G这样对于$\mathrm{1个}\le 我,j\le k$， 和$X\in V_{我}$,$\sum _{是\in V_j}d(X,是)$是一个常数。在这里我们表明$吨({米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H)$是一个$(H+\mathrm{1个})$-分区传输正则图。我们找到一个$(H+\mathrm{1个})\times (H+\mathrm{1个})$其最大特征值是距离谱半径的矩阵$吨({米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H)$. 我们得到的特征多项式$丁(吨({米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H))$根据较小的矩阵，并给出找到完整光谱的想法。此外，我们得到$丁(吨({米}_{\mathrm{1个}},{米}_{\mathrm{2个}},\dots \dots ,{米}_H))$有$-\mathrm{2个}$至少具有多重性的特征值${米}_{\mathrm{1个}}\cdots {米}_{H-\mathrm{1个}}({米}_H-\mathrm{1个})$和$-({米}_H+\mathrm{2个})\pm \sqrt{{米}_H({米}_H+\mathrm{4个})}$作为至少具有多重性的特征值${米}_{\mathrm{1个}}\cdots {米}_{H-\mathrm{2个}}({米}_{H-\mathrm{1个}}-\mathrm{1个})$.