Autobiographical notes
N.
Trinajstić
author
text
article
2017
eng
I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
231
257
http://ijmc.kashanu.ac.ir/article_45087_dcb8952d03d7c0cf9d02f509573121d2.pdf
dx.doi.org/10.22052/ijmc.2017.64354.1248
Graphs with smallest forgotten index
I.
Gutman
University of Kragujevac, Serbia
author
A.
Ghalavand
University of Kashan
author
T.
Dehghan-Zadeh
University of Kashan
author
A.
Ashrafi
University of Kashan
author
text
article
2017
eng
The forgotten topological index of a molecular graph $G$ is defined as $F(G)=\sum_{v\in V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $\gamma=1,2$, the first through the fourth for $\gamma=3$, and the first and the second for $\gamma=4,5$ are determined. These results are compared with those obtained for the first Zagreb index.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
259
273
http://ijmc.kashanu.ac.ir/article_43258_0b9303cff3a4e0713b73cf33798147fb.pdf
dx.doi.org/10.22052/ijmc.2017.43258
On the first variable Zagreb index
K.
Moradian
Department of Statistics, Islamic Azad University
author
R.
Kazemi
Imam Khomeini international university
author
M.
Behzadi
Department of Statistics, Islamic Azad University
author
text
article
2017
eng
The first variable Zagreb index of graph $G$ is defined as \begin{eqnarray*} M_{1,\lambda}(G)=\sum_{v\in V(G)}d(v)^{2\lambda}, \end{eqnarray*} where $\lambda$ is a real number and $d(v)$ is the degree of vertex $v$. In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees, plane-oriented recursive trees and binary increasing trees) are given.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
275
283
http://ijmc.kashanu.ac.ir/article_45113_2a098655d1e3c140f89c3276a97f9e78.pdf
dx.doi.org/10.22052/ijmc.2017.71544.1262
Computing the additive degree-Kirchhoff index with the Laplacian matrix
J.
Palacios
The University of New Mexico, Albuquerque, NM 87131, USA
author
text
article
2017
eng
For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
285
290
http://ijmc.kashanu.ac.ir/article_48532_3d7984d6e1bc469b6c8dc075c7bf9610.pdf
dx.doi.org/10.22052/ijmc.2017.64656.1249
On the spectra of reduced distance matrix of the generalized Bethe trees
A.
Heydari
Arak University of Technology
author
text
article
2017
eng
Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
291
298
http://ijmc.kashanu.ac.ir/article_48533_93ac14d2ea7c08d919a6c30039ff1ded.pdf
dx.doi.org/10.22052/ijmc.2017.30051.1116
On the second order first zagreb index
B
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
author
S.
Patil
Karnatak University
author
H. Y.
Deng
author
text
article
2017
eng
Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
299
311
http://ijmc.kashanu.ac.ir/article_49784_8a12c9b7c5c6942e17923e06c1f223ee.pdf
dx.doi.org/10.22052/ijmc.2017.83138.1284
Anti-forcing number of some specific graphs
S.
Alikhani
Yazd University, Yazd, Iran
author
N.
Soltani
Yazd University
author
text
article
2017
eng
Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specific graphs that are of importance in chemistry and study their anti-forcing numbers.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
313
325
http://ijmc.kashanu.ac.ir/article_49785_63810586ce414d4cc8a97c6dbf37dcb3.pdf
dx.doi.org/10.22052/ijmc.2017.60978.1235
On the forgotten topological index
A.
Khaksari
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
author
M.
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
author
text
article
2017
eng
The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
3
no.
2017
327
338
http://ijmc.kashanu.ac.ir/article_43481_12fee5261e77f9121b93d736c6102d79.pdf
dx.doi.org/10.22052/ijmc.2017.43481