通过增强型萨格勒布指数对图排序

Recently, Furtula et al. proposed a valuable predictive index in the study of the heat of formation in octanes and heptanes, the augmented Zagreb index(AZI index) of a graph G, which is defined as AZI(G) =∑uv∈E(G)( d_u d_v/d_u + d_v-2)~3,where E(G) is the edge set of G, d u and d v are the degrees of the terminal vertices u and v of edge uv, respectively. In this paper, we obtain the first five largest(resp., the first two smallest) AZI indices of connected graphs with n vertices. Moreover, we determine the trees of order n with the first three smallest AZI indices, the unicyclic graphs of order n with the minimum, the second minimum AZI indices, and the bicyclic graphs of order n with the minimum AZI index, respectively.

Ordering Graphs by the Augmented Zagreb Indices

Recently, Furtula et al. proposed a valuable predictive index in the study of the heat of formation in octanes and heptanes, the augmented Zagreb index (AZI index) of a graph $G$, which is defined as $$AZI(G)=sum_{uvin E(G)}big(frac{d_ud_v}{d_u+d_v-2}big)^3,$$ where $E(G)$ is the edge set of $G$, $d_u$ and $d_v$ are the degrees of the terminal vertices $u$ and $v$ of edge $uv$, respectively. In this paper, we obtain the first five largest (resp., the first two smallest) AZI indices of connected graphs with $n$ vertices. Moreover, we determine the trees of order $n$ with the first three smallest AZI indices, the unicyclic graphs of order $n$ with the minimum, the second minimum AZI indices, and the bicyclic graphs of order $n$ with the minimum AZI index, respectively.