Emeric Deutsch
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Emeric Deutsch has a total of 111 co-authors. Here are the top co-authors by number of shared publications:
David Callan
6 shared publications- Sandi Klavžar
University of Maribor
5 shared publications - Simone Rinaldi
Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Siena, Italy
5 shared publications - Sergi Elizalde
Department of Mathematics, Dartmouth College, Hanover, USA
4 shared publications - Luca Ferrari
Dipartimento di Matematica e Informatica "U. Dini" Università degli Studi di Firenze Firenze Italy
3 shared publications - A. J. Hildebrand
University of Illinois Urbana 61801 IL
2 shared publications
Latest Publications
- 22 April 2020
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 43 (6) , 4443-4456
On the Irregularity of $\pi $-Permutation Graphs, Fibonacci Cubes, and Trees- 22 April 2020
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 43 (6) , 4443-4456
On the Irregularity of $\pi $-Permutation Graphs, Fibonacci Cubes, and Trees- 14 August 2018
- Published by Springer Nature in Journal of Applied Mathematics and Computing
- Vol. 60 (1-2) , 253-264
M-polynomial revisited: Bethe cacti and an extension of Gutman’s approach
- 14 August 2018
- Published by Springer Nature in Journal of Applied Mathematics and Computing
- Vol. 60 (1-2) , 253-264
M-polynomial revisited: Bethe cacti and an extension of Gutman’s approach
- Open Access
M-Polynomial Revisited: Bethe Cacti and an Extension of Gutman's Approach
The $M$-polynomial of a graph $G$ is defined as $\sum_{i\le j} m_{i,j}(G)x^iy^j$, where $m_{i,j}(G)$, $i,j\ge 1$, is the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. Knowing the $M$-polynomial, formulas for bond incident degree indices (an important subclass of degree-based topological indices) can be obtained by means of specific operators defined on differentiable functions in two variables. This is illustrated on three infinite families of Bethe cacti. Gutman's approach for the computation of the coefficients of the $M$-polynomial is also recalled and an extension of it is given. This extension is used to determine the $M$-polynomial of a two-parameter infinite family of lattice graphs.Open AccessM-Polynomial Revisited: Bethe Cacti and an Extension of Gutman's Approach
The $M$-polynomial of a graph $G$ is defined as $\sum_{i\le j} m_{i,j}(G)x^iy^j$, where $m_{i,j}(G)$, $i,j\ge 1$, is the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. Knowing the $M$-polynomial, formulas for bond incident degree indices (an important subclass of degree-based topological indices) can be obtained by means of specific operators defined on differentiable functions in two variables. This is illustrated on three infinite families of Bethe cacti. Gutman's approach for the computation of the coefficients of the $M$-polynomial is also recalled and an extension of it is given. This extension is used to determine the $M$-polynomial of a two-parameter infinite family of lattice graphs. - Open Access
M-Polynomial and Degree-Based Topological Indices
Let $G$ be a graph and let $m_{ij}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The {\em $M$-polynomial} of $G$ is introduced with $\displaystyle{M(G;x,y) = \sum_{i\le j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples.Open AccessM-Polynomial and Degree-Based Topological Indices
Let $G$ be a graph and let $m_{ij}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The {\em $M$-polynomial} of $G$ is introduced with $\displaystyle{M(G;x,y) = \sum_{i\le j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples. - Open Access
The Hosoya polynomial of distance-regular graphs
In this note we obtain an explicit formula for the Hosoya polynomial of any distance-regular graph in terms of its intersection array. As a consequence, we obtain a very simple formula for the Hosoya polynomial of any strongly regular graph.
Open AccessThe Hosoya polynomial of distance-regular graphs
In this note we obtain an explicit formula for the Hosoya polynomial of any distance-regular graph in terms of its intersection array. As a consequence, we obtain a very simple formula for the Hosoya polynomial of any strongly regular graph.
- Open Access
Computing Hosoya polynomials of graphs from primary subgraphs
The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomials of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouquets of graphs, circuits of graphs and link of graphs. This is in turn applied to obtain the Hosoya polynomial of several chemically relevant families of graphs. In this way numerous known results are generalized and an approach to obtain them is simplified. Along the way several misprints from the literature are corrected.
Open AccessComputing Hosoya polynomials of graphs from primary subgraphs
The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomials of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouquets of graphs, circuits of graphs and link of graphs. This is in turn applied to obtain the Hosoya polynomial of several chemically relevant families of graphs. In this way numerous known results are generalized and an approach to obtain them is simplified. Along the way several misprints from the literature are corrected.
- 1 October 2012
- Published by Elsevier in Discrete Mathematics
- Vol. 312 (19) , 2927-2937
The run transform
- 1 October 2012
- Published by Elsevier in Discrete Mathematics
- Vol. 312 (19) , 2927-2937
The run transform
- 1 October 2012
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 160 (15) , 2314-2322
Rooted tree statistics from Matula numbers
- 1 October 2012
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 160 (15) , 2314-2322
Rooted tree statistics from Matula numbers
- 28 January 2012
- Published by Springer Nature in Annals of Combinatorics
- Vol. 16 (2) , 253-269
Restricted Simsun Permutations
- 28 January 2012
- Published by Springer Nature in Annals of Combinatorics
- Vol. 16 (2) , 253-269
Restricted Simsun Permutations
- 26 January 2012
- Published by Springer Nature in Annals of Combinatorics
- Vol. 16 (2) , 203-213
Adjacent q-Cycles in Permutations
- 26 January 2012
- Published by Springer Nature in Annals of Combinatorics
- Vol. 16 (2) , 203-213
Adjacent q-Cycles in Permutations