Multiplicative Zagreb eccentricity indices of some composite graphs

Luo, Zhaoyang; Wu, Jianliang

doi:10.22108/toc.2014.4988

تعداد نشریات	44
تعداد شماره‌ها	1,877
تعداد مقالات	15,278
تعداد مشاهده مقاله	43,732,108
تعداد دریافت فایل اصل مقاله	17,564,543

	Multiplicative Zagreb eccentricity indices of some composite graphs
Transactions on Combinatorics
مقاله 4، دوره 3، شماره 2، شهریور 2014، صفحه 21-29 اصل مقاله (321.23 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2014.4988
نویسندگان
Zhaoyang Luo¹؛ Jianliang Wu^* ²
¹B913, Zhixin Building School of Mathematics Shandong University 27 Shandananlu Rd.
²School of Mathematics, Shandong University
چکیده
Let $G$ be a connected graph‎. ‎The multiplicative Zagreb eccentricity indices of $G$ are defined respectively as ${\bf \Pi}_1^(G)=\prod_{v\in V(G)}\varepsilon_G^2(v)$ and ${\bf \Pi}_2^(G)=\prod_{uv\in E(G)}\varepsilon_G(u)\varepsilon_G(v)$‎, ‎where $\varepsilon_G(v)$ is the eccentricity of vertex $v$ in graph $G$ and $\varepsilon_G^2(v)=(\varepsilon_G(v))^2$‎. ‎In this paper‎, ‎we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of the factors and supply some exact expressions of ${\bf \Pi}_1^$ and ${\bf \Pi}_2^$ indices of some composite graphs‎, ‎such as the join‎, ‎disjunction‎, ‎symmetric difference and composition of graphs‎, ‎respectively‎.
کلیدواژه‌ها
Multiplicative Zagreb eccentricity indices؛ composite operations؛ Cartesian product

مراجع
K. C. Das, D. W. Lee and A. Graovac (2013) Some properties of the Zagreb eccentricity indices Ars Math. Contemp. 6, 117-125 N. De (2012) On multiplicative Zagreb eccenticity indices South Asian J. Math. 2 (6), 570-577 Z. Du, B. Zhou and N. Trinajstic (2012) Extremal properties of the Zagreb eccentricity indices Croat. Chem. Acta 85 (3), 359-362 M. Ghorbani and M. A. Hosseinzadeh (2012) A new version of Zagreb indices Filomat 26, 93-100 I. Gutman and N. Trinajstic (1972) Graph theory and molecular orbitals, Total pi electron energy of alternant hydrocarbons Chem. Phys. Lett. 17, 535-538 I. Gutman (2011) Multipicative Zagreb indices of trees Bull. Internat. Math. Virt. Inst. 1, 13-19 M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi (2009) The first and second Zagreb indices of some graph operations Discrete Appl. Math. 157, 804-811 R. Todeschini and V. Consonni (2010) New local vertex invariants and molecular descriptors based on functions of the vertex degree MATCH Commun. Math. Comput. Chem. 64, 359-372 D. Vukiucevic and A. Graovac (2010) Note on the comparison of the first and second normalized Zagreb eccentricity indices Acta Chim. Slov. 57, 524-528 D. B. West (1996) Introduction to Graph Theory second ed., Prentice Hall, Inc., Upper Saddle River, NJ R. Xing, B. Zhou and N. Trinajstic (2011) On Zagreb eccentricity indices Croat. Chem. Acta 84 (4), 493-497
آمار تعداد مشاهده مقاله: 4,084 تعداد دریافت فایل اصل مقاله: 3,007

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

Multiplicative Zagreb eccentricity indices of some composite graphs