Let G be a graph and d v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as Ra0(G)=åv Î V(G)dvaR_{alpha}^0(G)=sum_{vin V(G)}{d_{v}}^{alpha} where α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index Ra0(G)R_{alpha}^0(G) of conjugated unicyclic graphs G (i.e., unicyclic graphs with a perfect matching) and sharp lower and upper bounds are obtained for Ra0(G)R_{alpha}^0(G) depending on α in different intervals.
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机译：令G为图，d v 表示G中顶点v的度。图的零阶一般Randić索引定义为R a 0 （G）=å vÎV（G） d v a R_ {alpha} ^ 0（G）= sum_ {vin V（G）} {d_ {v}} ^ {alpha}其中α是任意实数。在本文中，我们研究了共轭单圈图G（即，零阶通用Randić指数R a 0 （G）R_ {alpha} ^ 0（G）根据不同的α，为R a 0 （G）R_ {alpha} ^ 0（G）获得具有完美匹配的单环图和上下限的尖锐间隔。
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