For a connected graph G and \(a,b \in \mathbb {R}\), the general degree-eccentricity index is defined as \(\mathrm{DEI}_{a,b}(G) = \sum _{v \in V(G)} d_{G}^{a}(v) \mathrm{ecc}_{G}^{b}(v)\), where V(G) is the vertex set of G, \(d_{G} (v)\) is the degree of a vertex v and \(\mathrm{ecc}_{G}(v)\) is the eccentricity of v in G. We obtain sharp upper and lower bounds on the general degree-eccentricity index for trees of given order in combination with given matching number, independence number, domination number or bipartition. The bounds hold for \(0< a < 1\) and \(b > 0\), or for \(a > 1\) and \(b < 0\). Many bounds hold also for \(a = 1\). All the extremal graphs are presented.

对于连接的图G和\（a，b \ in \ mathbb {R} \），一般的度偏心指数定义为\（\ mathrm {DEI} _ {a，b}（G）= \ sum _ {v \在v（G）} D_ {G} ^ {A}（v）\ mathrm {ECC} _ {G} ^ {b}（v）\），其中v（G ^）为顶点组的ģ，\（D_ {G}（v）\）是顶点的程度v和\（\ mathrm {ECC} _ {G}（v）\）是偏心v在ģ。对于给定顺序的树木，结合给定的匹配数，独立性数，支配数或二等分，我们获得了大致的度偏心率指数的上界和下界。边界保持\（0 <α<1 \）和\（B> 0 \） ，或用于\（A> 1 \）和\（B <0 \） 。\（a = 1 \）也有许多界限。给出了所有的极值图。