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 asAZI（G） = ∑uv∈E...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 asAZI（G） = ∑uv∈E（G）（dudv/du＋du-2）3,where E（G） is the edge set of G, d~ and d~ 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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11326221)
文摘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 asAZI（G） = ∑uv∈E（G）（dudv/du＋du-2）3,where E（G） is the edge set of G, d~ and d~ 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.
