University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
Autobiographical notes
231
257
EN
N.
Trinajstić
The Rugjer Bošković Institute and Croatian Academy of Sciences and Arts, Zagreb, Croatia
trina@irb.hr
10.22052/ijmc.2017.64354.1248
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).
Chemical graph theory,mathematical chemistry,Nanad Trinajstic
http://ijmc.kashanu.ac.ir/article_45087.html
http://ijmc.kashanu.ac.ir/article_45087_fe31c60ddad05b1f35c8ccaeb75be409.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
Graphs with smallest forgotten index
259
273
EN
I.
Gutman
University of Kragujevac, Serbia
gutman@kg.ac.rs
A.
Ghalavand
University of Kashan
ali797ghalavand@gmail.com
T.
Dehghan-Zadeh
University of Kashan
ta.dehghanzadeh@gmail.com
A.
R.
Ashrafi
University of Kashan
ijmc@kashanu.ac.ir
10.22052/ijmc.2017.43258
The forgotten topological index of a molecular graph $G$ is<br /> defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes<br /> the degree of vertex $u$ in $G$. The first through the sixth smallest<br /> forgotten indices among all trees, the first through<br /> the third smallest forgotten indices among all connected<br /> graph with cyclomatic number $gamma=1,2$, the first through<br /> the fourth for $gamma=3$, and the first and the second for<br /> $gamma=4,5$ are determined. These results are compared<br /> with those obtained for the first Zagreb index.
Forgotten topological index,Unicyclic graphs,Bicyclic graphs,Tricyclic graphs,Tetracyclic graphs,Pentacyclic graphs
http://ijmc.kashanu.ac.ir/article_43258.html
http://ijmc.kashanu.ac.ir/article_43258_60932aad8f9b423afed9a875153fe9a1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
On the first variable Zagreb index
275
283
EN
K.
Moradian
Department of Statistics, Islamic Azad University
rst.kazemi@gmail.com
R.
Kazemi
Imam Khomeini international university
r.kazemi@sci.ikiu.ac.ir
M.
H.
Behzadi
Department of Statistics, Islamic Azad University
behzadi.mh@gmail.com
10.22052/ijmc.2017.71544.1262
The first variable Zagreb index of graph $G$ is defined as<br /> begin{eqnarray*}<br /> M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda},<br /> end{eqnarray*}<br /> where $lambda$ is a real number and $d(v)$ is the degree of<br /> vertex $v$.<br /> In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees,<br /> plane-oriented recursive trees and binary increasing trees) are<br /> given.
First variable Zagreb index,Random increasing trees,Distribution function,Expected value
http://ijmc.kashanu.ac.ir/article_45113.html
http://ijmc.kashanu.ac.ir/article_45113_752ad28b4b442dc6a1f6961c8509c82a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
Computing the additive degree-Kirchhoff index with the Laplacian matrix
285
290
EN
J.
Palacios
The University of New Mexico, Albuquerque, NM 87131, USA
jpalacios@unm.edu
10.22052/ijmc.2017.64656.1249
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.
Degree-Kirchhoff index,Laplacian matrix
http://ijmc.kashanu.ac.ir/article_48532.html
http://ijmc.kashanu.ac.ir/article_48532_4ea24f618de4aee3f2e5feaf2ad0c8ca.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
On the spectra of reduced distance matrix of the generalized Bethe trees
291
298
EN
A.
Heydari
Arak University of Technology
a-heidari@iau-arak.ac.ir
10.22052/ijmc.2017.30051.1116
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.
Reduced distance matrix,Generalized Bethe Tree,spectrum
http://ijmc.kashanu.ac.ir/article_48533.html
http://ijmc.kashanu.ac.ir/article_48533_625a9813ec4456891441f9eb3d1369f5.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
On the second order first zagreb index
299
311
EN
B
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
b.basavanagoud@gmail.com
S.
Patil
Karnatak University
shreekantpatil949@gmail.com
H. Y.
Deng
Key Laboratoryof High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, P. R. China
hydeng@hunnu.edu.cn
10.22052/ijmc.2017.83138.1284
Inspired by the chemical applications of higher-order connectivity index (or<br /> Randic index), we consider here the higher-order first Zagreb index of a molecular graph.<br /> In this paper, we study the linear regression analysis of the second order first Zagreb<br /> index with the entropy and acentric factor of an octane isomers. The linear model, based<br /> on the second order first Zagreb index, is better than models corresponding to the first<br /> Zagreb index and F-index. Further, we compute the second order first Zagreb index of<br /> line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q],<br /> tadpole graphs, wheel graphs and ladder graphs.
topological index,line graph,subdivision graph,Nanostructure,tadpole graph
http://ijmc.kashanu.ac.ir/article_49784.html
http://ijmc.kashanu.ac.ir/article_49784_8354f7dae388f810624e8396d0fc4b3a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
Anti-forcing number of some specific graphs
313
325
EN
S.
Alikhani
Yazd University, Yazd, Iran
alikhani@yazd.ac.ir
N.
Soltani
Yazd University
neda_soltani@ymail.com
10.22052/ijmc.2017.60978.1235
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 <br /> their anti-forcing numbers.
Anti-forcing number,Anti-forcing set,Corona product
http://ijmc.kashanu.ac.ir/article_49785.html
http://ijmc.kashanu.ac.ir/article_49785_5762b32f4d73311e1b30d195fe19f9ba.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
3
2017
09
01
On the forgotten topological index
327
338
EN
A.
Khaksari
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
khm.paper@gmail.com
M.
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
mghorbani@sru.ac.ir
10.22052/ijmc.2017.43481
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.
Zagreb indices,forgotten index,Graph products
http://ijmc.kashanu.ac.ir/article_43481.html
http://ijmc.kashanu.ac.ir/article_43481_e5cf8939aefd37aece3fc2f3f7bd8375.pdf