CMMSE: A new approximation to the geometric–arithmetic index

The concept of geometric–arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric–arithmetic index \(GA_1\) and characterize graphs extremal with respect to them.     

The Hosoya index and the Merrifield–Simmons index

In this article, we give sharp bounds on the Hosoya index and the Merrifield–Simmons index for connected graphs of fixed size. As a consequence, we determine all connected graphs of any fixed order and size which maximize the Merrifield–Simmons index. Sharp lower bounds on the Hosoya index are known for graphs of order n and size \(m\in [n-1,2n-3]\cup \left( {n-1\atopwithdelims ()2},{n\atopwithdelims ()2}\right] \); while sharp upper bounds were only known for graphs of order n and size \(m\le n+2\). We give sharp upper bounds on the Hosoya index for dense graphs with \(m\ge {n\atopwithdelims ()2}-2n/3\). Moreover, all extreme graphs are also determined.     

Author Index to Volume 24, 2006

ALI,A.,1 547ALI,Syed Mashhood,665AN,Yu,401;1 375AN,Zhong·Wei,1 754ANBIA,Mansur,1026AO,Li一Mei,253ASMAT)Fahmeena,665ATAV,Ulfet,603BAI,Chen一Xi,1 639BAI,Ji·Hai,360BAI,Zhu,1 24BALUJA,ShiPra,1327BAO,Han,481BAO,Hua一Ying,355BAO,Ren一Lie,1 001BAO,Xiao一Ling,85BERNATH,G巨bor,1792Bl,Cai一Feng,371B IAN,Liu一Jiao,653BLECHERT,Siegfried,1080BOKROS,Attila,1792CHANG,Jia一Zhong,1255CHANG,Lih一Wei,1238CHANG,Li·Qun,1 214CHEN,Bao一Quan,99CHEN,Bing,463CH…