# Seyyed Aliasghar HosseiniSimon Fraser University · Department of Mathematics

Seyyed Aliasghar Hosseini

PhD

## About

24

Publications

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331

Citations

Introduction

Additional affiliations

September 2007 - August 2013

## Publications

Publications (24)

The weighted Szeged index is a recent extension of the well-known Szeged index. Trees are conjectured to achieve the minimum weighted Szeged index among all graphs with a given number of vertices. In this paper, we present new tools to analyze and characterize trees with minimum weighted Szeged index. We exhibit the best trees with up to 130 vertic...

We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in particular, that the cop number of any graph with girth g $g$ and minimum degree δ $\delta $ is at least 1 g ( δ − 1 ) ⌊ g − 1 4 ⌋ $\frac{1}{g}{(\delta -1)}^{\lfloor \frac{g-1}...

We show that the cop number of directed and undirected Cayley graphs on abelian groups is in O(n), where n is the number of vertices, by introducing a refined inductive method. With our method, we improve the previous upper bound on cop number for undirected Cayley graphs on abelian groups, and we establish an upper bound on the cop number of direc...

The game of Cops and Robbers is a well‐known pursuit‐evasion game played on graphs. It has been proved that cubic graphs can have arbitrarily large cop number c ( G ), but the known constructions show only that the set { c ( G ) ∣ G cubic } is unbounded. In this paper, we prove that there are arbitrarily large subcubic graphs G whose cop number is...

The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.

Weighted Szeged index is a recently introduced extension of the well-known Szeged index. In this paper, we present a new tool to analyze and characterize minimum weighted Szeged index trees. We exhibit the best trees with up to 81 vertices and use this information, together with our results, to propose various conjectures on the structure of minimu...

We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in particular, that the cop number of any graph with girth $g$ and minimum degree $\delta$ is at least $\tfrac{1}{g}(\delta - 1)^{\lfloor \frac{g-1}{4}\rfloor}$. We establish simi...

The game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previously used probabilistic method which results in an improved upper bound for the cop number of graphs of bounded diameter. In particular, for graphs of diameter four, we impr...

The game of Cops and Robbers is a well known pursuit-evasion game played on graphs. It has been proved \cite{bounded_degree} that cubic graphs can have arbitrarily large cop number $c(G)$, but the known constructions show only that the set $\{c(G) \mid G \text{ cubic}\}$ is unbounded. In this paper we prove that there are arbitrarily large subcubic...

We consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal graphs, and outerplanar graphs. We also obtain improved bounds for bipartite planar and toroidal graphs. We briefly consider general graphs of bounded genus.

We show that the cop number of directed and undirected Cayley graphs on abelian groups has an upper bound of the form of $O(\sqrt{n})$, where $n$ is the number of vertices, by introducing a refined inductive method. With our method, we improve the previous upper bound on cop number for undirected Cayley graphs on abelian groups, and we establish an...

Arboricity is a graph parameter akin to chromatic number, in that it seeks to partition the vertices into the smallest number of sparse subgraphs. Where for the chromatic number we are partitioning the vertices into independent sets, for the arboricity we want to partition the vertices into cycle-free subsets (i.e., forests). Arboricity is NP-hard...

The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.

The game of cops and robbers is a pursuit game on graphs where a set of agents, called the cops try to get to the same position of another agent, called the robber. Cops and robbers has been studies on several classes of graphs including geometrically represented graphs. For example, it has been shown that string graphs, including geometric graphs,...

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and is considered by some as one of the most intriguing open problems in mathematical chemistry. In this paper, we describe t...

The game of Cops and Robbers is a very well known game played on graphs. In this paper we will show that minimum order of a graph that needs k cops to guarantee the robber’s capture is increasing in k.

The integer grid Z□Z has four typical orientations of its edges which make it a vertex-transitive digraph. In this paper we analyze the game of Cops and Robbers on arbitrary finite quotients of these directed grids.

In 1999, De Simone and K\"{o}rner conjectured that every graph without
induced $C_5,C_7,\overline{C}_7$ contains a clique cover $\mathcal C$ and a
stable set cover $\mathcal I$ such that every clique in $\mathcal C$ and every
stable set in $\mathcal I$ have a vertex in common. This conjecture has roots
in information theory and became known as the...

The problem of complete characterization of trees with minimal atom-bond connectivity (ABC) index is still an open problem. In [21], a conjecture on the structure of the trees with minimal ABC index, based on the assumption of existence of a central vertex, was posed. This conjecture was partially disproved in [1, 2], and subsequently in [12], whic...

In the class of Kragujevac trees, the elements having minimal atom-bond connectivity index are determined. By this, an earlier conjecture [MATCH Commun. Math. Comput. Chem. 68 (2012) 131-136] is confirmed and slightly corrected.

The atom-bond connectivity (ABC) index of a graph G is defined as the sum over all pairs of adjacent vertices u, v, of the terms root[d(u) + d(v) - 2]/[d(u) d(v)], where d(v) denotes the degree of the vertex v of the graph G. Whereas the finding of the graphs with the greatest ABC-value is an easy task, the characterization of the graphs with small...

Finding trees with minimal atom-bond connectivity (ABC) index, in the general case, is still an open problem. I. M. Gutman and B. Furtula [MATCH Commun. Math. Comput. Chem. 68, No. 1, 131–136 (2012; Zbl 1289.05047)] posed a conjecture on the structure of trees with a single high-degree vertex and smallest ABC index. Here we find a case when this co...

Finding trees with minimal atom-bond connectivity (ABC) index, in the general case, is
still an open problem. I. Gutman and B. Furtula [MATCH Commun. Math. Comput. Chem. 86
(2012) 131-136] posed a conjecture on the structure of trees with a single high-degree vertex
and smallest ABC index. Here we find a case when this conjecture fails for trees wi...