پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,877 |
| تعداد مقالات | 15,278 |
| تعداد مشاهده مقاله | 43,731,182 |
| تعداد دریافت فایل اصل مقاله | 17,563,278 |
Complete solution to a conjecture of Zhang-Liu-Zhou | ||
| Transactions on Combinatorics | ||
| مقاله 21، دوره 3، شماره 4، اسفند 2014، صفحه 55-58 اصل مقاله (473.15 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.5986 | ||
| نویسندگان | ||
| Mostafa Tavakoli* 1؛ F. Rahbarnia1؛ M. Mirzavaziri1؛ A. R. Ashrafi2 | ||
| 1Ferdowsi University of Mashhad | ||
| 2University of Kashan | ||
| چکیده | ||
| Let $d_{n,m}=\big[\frac{2n+1-\sqrt{17+8(m-n)}}{2}\big]$ and $E_{n,m}$ be the graph obtained from a path $P_{d_{n,m}+1}=v_0v_1 \cdots v_{d_{n,m}}$ by joining each vertex of $K_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$, and by joining $m-n+1-{n-d_{n,m}\choose 2}$ vertices of $K_{n-d_{n,m}-1}$ to $v_{d_{n,m}-2}$. Zhang, Liu and Zhou [On the maximal eccentric connectivity indices of graphs, Appl. Math. J. Chinese Univ., in press] conjectured that if $d_{n,m}\geqslant 3$, then $E_{n,m}$ is the graph with maximal eccentric connectivity index among all connected graph with $n$ vertices and $m$ edges. In this note, we prove this conjecture. Moreover, we present the graph with maximal eccentric connectivity index among the connected graphs with $n$ vertices. Finally, the minimum of this graph invariant in the classes of tricyclic and tetracyclic graphs are computed. | ||
| کلیدواژهها | ||
| Eccentric connectivity index؛ tricyclic graph؛ tetracyclic graph؛ graph operation | ||
| مراجع | ||
|
D. B. West (1996) Introduction to G raph Theory Prentice Hall, Inc., Upper Saddle River, NJ
V. Sharma, R. Goswami and A. K. Madan (1997) Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies J. Chem. Inf. Comput. Sci. 37, 273-282
A. R. Ashrafi, T. Doslic and M. Saheli (2011) The eccentric connectivity index of TUC4 C8 (R) nanotubes MATCH Commun. Math. Comput. Chem. 65 (1), 221-230
A. R. Ashrafi, M. Saheli and M. Ghorbani (2011) The eccentric connectivity index of nanotubes and nanotori J. Comput. Appl. Math. 235, 4561-4566
G. Yu, L. Feng and A. Ilic (2011) On the eccentric distance sum of trees and unicyclic graphs J. Math. Anal. Appl. 375, 99-107
B. Zhou and Z. Du (2010) On eccentric connectivity index MATCH Commun. Math. Comput. Chem. 63, 181-198
A. Ilic and I. Gutman (2011) Eccentric connectivity index of chemical trees MATCH Commun. Math. Comput. Chem. 65, 731-744
M. J. Morgan, S. Mukwembi and H. C. Swart (2011) On the eccentric connectivity index of a graph Discrete Math. 311, 1229-1234
T. Doslic, M. Saheli and D. Vukicevic (2010) Eccentric Connectivity Index: Extremal Graphs and Values Iranian J. Math. Chem. 1 (2), 45-56
J. Zhang, Z. Liu and B. Zhou (in press) On the maximal eccentric connectivity indices of graphs Appl. Math. J. Chinese Univ.
| ||
|
آمار تعداد مشاهده مقاله: 4,530 تعداد دریافت فایل اصل مقاله: 3,092 |
||