TY - JOUR AU - Zuki, Wan Nor Nabila Nadia Wan AU - Hasni, Roslan AU - Husin, Nor Hafizah Md. AU - Du, Zhibin AU - Raheem, Abdul PY - 2021 TI - On the difference between geometric-arithmetic index and atom-bond connectivity index for trees JO - Journal of Mathematics and Computer Science SP - 49--58 VL - 22 IS - 1 AB - Let \(G\) be a simple and connected graph with vertex set \(V(G)\) and edge set \(E(G)\). The geometric-arithmetic index and atom-bond connectivity index of graph \(G\) are defined as \(GA(G)=\sum_{uv\in E(G)} \frac{2\sqrt{d_ud_v}}{d_u + d_v}\) and \(ABC(G)=\sum_{uv\in E(G)} \sqrt{\frac{d_u+d_v-2}{d_ud_v}}\), respectively, where the summation extends over all edges \(uv\) of \(G\), and \(d_u\) denotes the degree of vertex \(u\) in \(G\). Let \((GA-ABC)(G)\) denote the difference between \(GA\) and \(ABC\) indices of \(G\). In this note, we determine \(n\)-vertex binary trees with first three minimum \(GA-ABC\) values. We also present a lower bound for \(GA-ABC\) index of molecular trees with fixed number of pendant vertices. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.022.01.05 DO - 10.22436/jmcs.022.01.05 ID - Zuki2021 ER - TY - JOUR TI - On the difference between atom-bond connectivity index and Randic index of binary and chemical trees AU - A. Ali AU - Z. Du JO - Int. J. Quantum Chem. PY - 2017 DA - 2017// VL - 117 ID - Ali2017 ER - TY - JOUR TI - The maximum atom-bond connectivity index for graphs with edge-connectivity one AU - Q. Cui AU - Q. P. Qian AU - L. P. Zhong JO - Discrete Appl. Math. PY - 2017 DA - 2017// VL - 220 ID - Cui2017 ER - TY - JOUR TI - On geometric-arithmetic index of graphs AU - K. C. Das JO - MATCH Commun. Math. Comput. Chem. PY - 2010 DA - 2010// VL - 64 ID - Das2010 ER - TY - JOUR TI - On the first geometric-arithmetic index of graphs AU - K. C. Das AU - I. Gutman AU - B. Furtula JO - Discrete Appl. Math. PY - 2011 DA - 2011// VL - 159 ID - Das2011 ER - TY - JOUR TI - Survey on geometric-arithmetic indices of graphs AU - K. C. Das AU - I. Gutman AU - B. Furtula JO - MATCH Commun. Math. Comput. Chem. PY - 2011 DA - 2011// VL - 65 ID - Das2011 ER - TY - JOUR TI - Comparison between the first geometric-arithmetic index and atom-bond connectivity index AU - K. C. Das AU - N. Trinajstić JO - Chem. Phsy. Lett. PY - 2010 DA - 2010// VL - 497 ID - Das2010 ER - TY - BOOK TI - Topological indices and related descriptors in QSAR and QSPAR AU - J. Devillers AU - A. T. Balaban PB - Gordon and Breach PY - 1999 DA - 1999// CY - Amsterdam ID - Devillers1999 ER - TY - JOUR TI - On the structural properties of trees with minimal atom-bond connectivity index III: Bounds on $B_1$- and $B_2$-branches AU - D. Dimitrov JO - Discrete Appl. Math. PY - 2016 DA - 2016// VL - 204 ID - Dimitrov2016 ER - TY - JOUR TI - Atom-bond connectivity and energetic of branched alkanes AU - E. Estrada JO - Chem. Phsy. Lett. PY - 2008 DA - 2008// VL - 463 ID - Estrada2008 ER - TY - JOUR TI - An atom-bond connectivity index: modelling the enthalpy of formation of alkanes AU - E. Estrada AU - L. Torres AU - L. Rodriguez AU - I. Gutman JO - Indian J. Chem. Sect. A PY - 1998 DA - 1998// VL - 37 ID - Estrada1998 ER - TY - JOUR TI - The smallest $ABC$ index of trees with $n$ pendant vertices AU - Y. Gao AU - Y. Shao JO - MATCH Commun. Math. Comput. Chem. PY - 2016 DA - 2016// VL - 76 ID - Gao2016 ER - TY - JOUR TI - Atom-bond connectivity and geometric-arithmetic indices in random polyphenyl chain AU - X. Ke JO - submitted PY - DA - // VL - ID - Ke ER - TY - JOUR TI - More comparison between the first geometric-arithmetic index and atom-bond connectivity index AU - Z. Raza AU - A. A. Bhatti AU - A. Ali JO - Miskolc Math. Notes PY - 2016 DA - 2016// VL - 17 ID - Raza2016 ER - TY - JOUR TI - Spectral properties of geometric-arithmetic index AU - J. M. Rodriguez AU - J. M. Sigarreta JO - Appl. Math. Comput. PY - 2016 DA - 2016// VL - 277 ID - Rodriguez2016 ER - TY - JOUR TI - On the maximum $ABC$ index of graphs without pendent vertices AU - Z. H. Shao AU - P. Wu AU - Y. Y. Gao AU - I. Gutman AU - X. J. Zhang JO - Appl. Math. Comput. PY - 2017 DA - 2017// VL - 315 ID - Shao2017 ER - TY - BOOK TI - Handbook of molecular descriptors AU - R. Todeschini AU - V. Consonni PB - Wiley-VCH PY - 2000 DA - 2000// CY - Weinheim ID - Todeschini2000 ER - TY - JOUR TI - Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges AU - D. Vukičević AU - B. Furtula JO - J. Math. Chem. PY - 2009 DA - 2009// VL - 46 ID - Vukičević2009 ER - TY - JOUR TI - Comparing the excepted values of atom-bond connectivity and geometric-arithmetic indices in random spiro chains AU - S. L. Wei AU - X. L. Ke AU - G. L. Hao JO - J. Inequal. Appl. PY - 2018 DA - 2018// VL - 2018 ID - Wei2018 ER - TY - BOOK TI - Introduction to Graph Theory AU - D. B. West PB - Prentice-Hall PY - 2001 DA - 2001// CY - Upper Saddle River ID - West2001 ER - TY - JOUR TI - On the atom-bond connectivity index of connected graphs AU - R. Xing AU - B. Zhou AU - F. M. Dong JO - Discrete Appl. Math. PY - 2011 DA - 2011// VL - 159 ID - Xing2011 ER - TY - JOUR TI - On geometric-arithmetic index AU - Y. Yuan AU - B. Zhou AU - N. Trinajstić JO - J. Math. Chem. PY - 2010 DA - 2010// VL - 47 ID - Yuan2010 ER - TY - JOUR TI - On a relation between the atom-bond connectivity and the first geometric-arithmetic indices AU - L. P. Zhong AU - Q. Cui JO - Discrete Appl. Math. PY - 2015 DA - 2015// VL - 185 ID - Zhong2015 ER -