ORIGINAL_ARTICLE
Autobiographical notes
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).
http://ijmc.kashanu.ac.ir/article_45087_dcb8952d03d7c0cf9d02f509573121d2.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
231
257
10.22052/ijmc.2017.64354.1248
Chemical graph theory
mathematical chemistry
Nanad Trinajstic
N.
Trinajstić
trina@irb.hr
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Graphs with smallest forgotten index
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.
http://ijmc.kashanu.ac.ir/article_43258_0b9303cff3a4e0713b73cf33798147fb.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
259
273
10.22052/ijmc.2017.43258
Forgotten topological index
Unicyclic graphs
Bicyclic graphs
Tricyclic graphs
Tetracyclic graphs
Pentacyclic graphs
I.
Gutman
gutman@kg.ac.rs
true
1
University of Kragujevac, Serbia
University of Kragujevac, Serbia
University of Kragujevac, Serbia
AUTHOR
A.
Ghalavand
ali797ghalavand@gmail.com
true
2
University of Kashan
University of Kashan
University of Kashan
AUTHOR
T.
Dehghan-Zadeh
ta.dehghanzadeh@gmail.com
true
3
University of Kashan
University of Kashan
University of Kashan
AUTHOR
A.
Ashrafi
ijmc@kashanu.ac.ir
true
4
University of Kashan
University of Kashan
University of Kashan
LEAD_AUTHOR
ORIGINAL_ARTICLE
On the first variable Zagreb index
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.
http://ijmc.kashanu.ac.ir/article_45113_2a098655d1e3c140f89c3276a97f9e78.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
275
283
10.22052/ijmc.2017.71544.1262
First variable Zagreb index
Random increasing trees
Distribution function
Expected value
K.
Moradian
rst.kazemi@gmail.com
true
1
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
AUTHOR
R.
Kazemi
r.kazemi@sci.ikiu.ac.ir
true
2
Imam Khomeini international university
Imam Khomeini international university
Imam Khomeini international university
LEAD_AUTHOR
M.
Behzadi
behzadi.mh@gmail.com
true
3
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
AUTHOR
ORIGINAL_ARTICLE
Computing the additive degree-Kirchhoff index with the Laplacian matrix
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.
http://ijmc.kashanu.ac.ir/article_48532_3d7984d6e1bc469b6c8dc075c7bf9610.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
285
290
10.22052/ijmc.2017.64656.1249
Degree-Kirchhoff index
Laplacian matrix
J.
Palacios
jpalacios@unm.edu
true
1
The University of New Mexico, Albuquerque, NM 87131, USA
The University of New Mexico, Albuquerque, NM 87131, USA
The University of New Mexico, Albuquerque, NM 87131, USA
LEAD_AUTHOR
ORIGINAL_ARTICLE
On the spectra of reduced distance matrix of the generalized Bethe trees
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.
http://ijmc.kashanu.ac.ir/article_48533_93ac14d2ea7c08d919a6c30039ff1ded.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
291
298
10.22052/ijmc.2017.30051.1116
Reduced distance matrix
Generalized Bethe Tree
spectrum
A.
Heydari
a-heidari@iau-arak.ac.ir
true
1
Arak University of Technology
Arak University of Technology
Arak University of Technology
LEAD_AUTHOR
ORIGINAL_ARTICLE
On the second order first zagreb index
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.
http://ijmc.kashanu.ac.ir/article_49784_8a12c9b7c5c6942e17923e06c1f223ee.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
299
311
10.22052/ijmc.2017.83138.1284
Topological index
line graph
subdivision graph
Nanostructure
tadpole graph
B
Basavanagoud
b.basavanagoud@gmail.com
true
1
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
AUTHOR
S.
Patil
shreekantpatil949@gmail.com
true
2
Karnatak University
Karnatak University
Karnatak University
AUTHOR
H. Y.
Deng
hydeng@hunnu.edu.cn
true
3
LEAD_AUTHOR
ORIGINAL_ARTICLE
Anti-forcing number of some specific graphs
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.
http://ijmc.kashanu.ac.ir/article_49785_63810586ce414d4cc8a97c6dbf37dcb3.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
313
325
10.22052/ijmc.2017.60978.1235
Anti-forcing number
Anti-forcing set
Corona product
S.
Alikhani
alikhani@yazd.ac.ir
true
1
Yazd University, Yazd, Iran
Yazd University, Yazd, Iran
Yazd University, Yazd, Iran
LEAD_AUTHOR
N.
Soltani
neda_soltani@ymail.com
true
2
Yazd University
Yazd University
Yazd University
AUTHOR
ORIGINAL_ARTICLE
On the forgotten topological index
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.
http://ijmc.kashanu.ac.ir/article_43481_12fee5261e77f9121b93d736c6102d79.pdf
2017-09-01T11:23:20
2018-02-22T11:23:20
327
338
10.22052/ijmc.2017.43481
Zagreb indices
Forgotten index
Graph products
A.
Khaksari
khm.paper@gmail.com
true
1
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
AUTHOR
M.
Ghorbani
mghorbani@srttu.edu
true
2
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee Teacher Training University
LEAD_AUTHOR