Papers by Tomislav Došlić
Fusene chains revisited: how kinky they are and why it matters
Journal of mathematical chemistry, May 7, 2024
Linear Algebra and its Applications, Sep 1, 2010
For a given graph G its Szeged weighting is defined by w(e) = n u (e)n v (e), where e = uv is an ... more For a given graph G its Szeged weighting is defined by w(e) = n u (e)n v (e), where e = uv is an edge of G, n u (e) is the number of vertices of G closer to u than to v, and n v (e) is defined analogously. The adjacency matrix of a graph weighted in this way is called its Szeged matrix. In this paper we determine the spectra of Szeged matrices and their Laplacians for several families of graphs. We also present sharp upper and lower bounds on the eigenvalues of Szeged matrices of graphs.
Match-communications in Mathematical and in Computer Chemistry, 2016
We use recently obtained lower bounds on the independence number of fullerene graphs to settle in... more We use recently obtained lower bounds on the independence number of fullerene graphs to settle in affirmative a conjecture of the Graffiti software about the relationship between the independence number and the face independence number of a fullerene graph. We also consider another Graffiti conjecture, concerned with the relationship of the independence number and the radius of a fullerene graph, and show that it is not valid.
Match-communications in Mathematical and in Computer Chemistry, 2016
We use recently obtained lower bounds on the independence number of fullerene graphs to settle in... more We use recently obtained lower bounds on the independence number of fullerene graphs to settle in affirmative a conjecture of the Graffiti software about the relationship between the independence number and the face independence number of a fullerene graph. We also consider another Graffiti conjecture, concerned with the relationship of the independence number and the radius of a fullerene graph, and show that it is not valid.
Iranian journal of mathematical chemistry, Mar 1, 2013
In this paper we present explicit formulas for the eccentric connectivity index of three classes ... more In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.
Perfect Matchings, Catalan Numbers, and Pascal's Triangle
Mathematics Magazine, Jun 1, 2007
ABSTRACT
Factor-critical graphs with the minimum number of near-perfect matchings
Discrete Mathematics, Dec 1, 2015
We show that a factor-critical graph of order n has exactly n near-perfect matchings if and only ... more We show that a factor-critical graph of order n has exactly n near-perfect matchings if and only if it is a connected graph whose blocks are all odd cycles. This characterizes the factor-critical graphs with the minimum number of near-perfect matchings.
Shortest perfect pseudomatchings in fullerene graphs
Applied Mathematics and Computation, Jul 1, 2022
Iranian journal of mathematical chemistry, Mar 1, 2017
We show how generalized Zagreb indices M 1 k (G) can be computed by using a simple graph polynomi... more We show how generalized Zagreb indices M 1 k (G) can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.
Discrete Mathematics, Jun 1, 2008
The structural theory of matchings is used to establish lower bounds on the number of perfect mat... more The structural theory of matchings is used to establish lower bounds on the number of perfect matchings in n-extendable graphs. It is shown that any such graph on p vertices and q edges contains at least (n + 1)!/4[qp -(n -1)(2 -3) + 4] different perfect matchings, where is the maximum degree of a vertex in G.
Global forcing number for maximal matchings
Discrete Mathematics, Mar 1, 2018
Abstract Let M ( G ) denote the set of all maximal matchings in a simple graph G , and f : M ( G ... more Abstract Let M ( G ) denote the set of all maximal matchings in a simple graph G , and f : M ( G ) → { 0 , 1 } | E ( G ) | be the characteristic function of maximal matchings of G . Any set S ⊆ E ( G ) such that f | S is an injection is called a global forcing set for maximal matchings in G , and the cardinality of smallest such S is called the global forcing number for maximal matchings of G . In this paper we establish sharp lower and upper bounds on this quantity and prove explicit formulas for certain classes of graphs. At the end, we also state some open problems and discuss some further developments.
Croatica Chemica Acta, Jun 15, 2005
In the first part of this paper it is shown how to use ear decomposition techniques in proving ex... more In the first part of this paper it is shown how to use ear decomposition techniques in proving existence and establishing lower bounds to the number of perfect matchings in lattice animals. A correspondence is then established between perfect matchings in certain classes of benzenoid graphs and paths in the rectangular lattice that satisfy certain diagonal constraints. This correspondence is used to give explicit formulas for the number of perfect matchings in hexagonal benzenoid graphs and to derive some identities involving Fibonacci numbers and binomial coefficients. Some of the results about benzenoid graphs are also translated into the context of polyominoes.
Journal of Mathematical Inequalities, 2009
A sequence (x n ) n 0 of positive real numbers is log-convex if the inequality x 2 n x n-1 x n+1 ... more A sequence (x n ) n 0 of positive real numbers is log-convex if the inequality x 2 n x n-1 x n+1 is valid for all n 1 . We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.
Discussiones Mathematicae Graph Theory, 2005
It is shown in this note that some matching-related properties of graphs, such as their factor-cr... more It is shown in this note that some matching-related properties of graphs, such as their factor-criticality, regularizability and the existence of perfect 2-matchings, are preserved when iterating Mycielski's construction.
Eccentric connectivity index of graphs with subdivided edges
Electronic Notes in Discrete Mathematics, 2014
ABSTRACT We consider four classes of graphs arising from a given graph via different types of edg... more ABSTRACT We consider four classes of graphs arising from a given graph via different types of edge subdivisions. We present explicit formulas expressing their eccentric connectivity index in terms of the eccentric connectivity index of the original graph and some auxiliary invariants.
Discrete Applied Mathematics, May 1, 2007
Bipartite edge frustration of a graph is defined as the smallest number of edges that have to be ... more Bipartite edge frustration of a graph is defined as the smallest number of edges that have to be deleted from the graph to obtain a bipartite spanning subgraph. We show that for fullerene graphs this quantity can be computed in polynomial time and obtain explicit formulas for the icosahedral fullerenes. We also report some computational results and discuss a potential application of this invariant in the context of fullerene stability.
On biregular planar triangulations
The paper is concerned with the existence of biregular planar triangulations on a given number of... more The paper is concerned with the existence of biregular planar triangulations on a given number of vertices. It is shown that an (r, s)-regular planar triangulation on n vertices exists for all n > 13 if and only if s=6 and r=4 or r=5.
Discrete Applied Mathematics, Jul 1, 2010
The smallest number of edges that have to be deleted from a graph to obtain a bipartite spanning ... more The smallest number of edges that have to be deleted from a graph to obtain a bipartite spanning subgraph is called the bipartite edge frustration of G and denoted by ϕ(G). In this paper we determine the bipartite edge frustration of some classes of composite graphs.
arXiv (Cornell University), Apr 24, 2023
arXiv (Cornell University), Dec 13, 2022
We prove a master identity for a class of sequences defined by full-history linear homogeneous re... more We prove a master identity for a class of sequences defined by full-history linear homogeneous recurrences with (non-negative) constant coefficients. The identity is derived in a combinatorial way, providing thus combinatorial proofs for many known and new identities obtained as its corollaries. In particular, we prove several interesting identities for the Pell, the Jacobsthal, and the m-nacci numbers.
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Papers by Tomislav Došlić