2017
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Autobiographical notes
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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).
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N.
Trinajstić
Croatia
trina@irb.hr
Chemical graph theory
mathematical chemistry
Nanad Trinajstic
Graphs with smallest forgotten index
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The forgotten topological index of a molecular graph $G$ is defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, 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.
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273


I.
Gutman
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia
gutman@kg.ac.rs


A.
Ghalavand
University of Kashan
University of Kashan
I R Iran
ali797ghalavand@gmail.com


T.
DehghanZadeh
University of Kashan
University of Kashan
I R Iran
ta.dehghanzadeh@gmail.com


A.
Ashrafi
University of Kashan
University of Kashan
I R Iran
ijmc@kashanu.ac.ir
Forgotten topological index
Unicyclic graphs
Bicyclic graphs
Tricyclic graphs
Tetracyclic graphs
Pentacyclic graphs
On the first variable Zagreb index
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The first variable Zagreb index of graph $G$ is defined as begin{eqnarray*} M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda}, 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, planeoriented recursive trees and binary increasing trees) are given.
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275
283


K.
Moradian
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
I R Iran
rst.kazemi@gmail.com


R.
Kazemi
Imam Khomeini international university
Imam Khomeini international university
I R Iran
r.kazemi@sci.ikiu.ac.ir


M.
Behzadi
Department of Statistics, Islamic Azad University
Department of Statistics, Islamic Azad University
I R Iran
behzadi.mh@gmail.com
First variable Zagreb index
Random increasing trees
Distribution function
Expected value
Computing the additive degreeKirchhoff index with the Laplacian matrix
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For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degreeKirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degreeKirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.
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285
290


J.
Palacio
The University of New Mexico, Albuquerque, NM 87131, USA
The University of New Mexico, Albuquerque,
Iran
jpalacios@unm.edu
DegreeKirchhoff index
Laplacian matrix
On the spectra of reduced distance matrix of the generalized Bethe trees
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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.
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298


A.
Heydari
Arak University of Technology
Arak University of Technology
I R Iran
aheidari@iauarak.ac.ir
Reduced distance matrix
Generalized Bethe Tree
Spectrum
On the second order first zagreb index
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Inspired by the chemical applications of higherorder connectivity index (or Randic index), we consider here the higherorder 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 Findex. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2Dlattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.
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B
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
India
b.basavanagoud@gmail.com


S.
Patil
Karnatak University
Karnatak University
India
shreekantpatil949@gmail.com


H. Y.
Deng
Iran
hydeng@hunnu.edu.cn
Topological index
line graph
subdivision graph
nanostructure
tadpole graph
Antiforcing number of some specific graphs
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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 antiforcing 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 antiforcing numbers.
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325


S.
Alikhani
Yazd University, Yazd, Iran
Yazd University, Yazd, Iran
I R Iran
alikhani@yazd.ac.ir


N.
Soltani
Yazd University
Yazd University
I R Iran
neda_soltani@ymail.com
Antiforcing number
Antiforcing set
Corona product
On the forgotten topological index
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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.
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A.
Khaksari
Department of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. Iran
Department of Mathematics, Payame Noor University,
I R Iran
khm.paper@gmail.com


M.
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee
I R Iran
mghorbani@srttu.edu
Zagreb indices
Forgotten index
Graph products