The thinness of a graph is width parameter that generalizes some properties interval graphs, which are exactly the graphs one. Many NP-complete problems can be solved in polynomial time for with bounded thinness, given suitable representation graph. In this paper we study and its variations products. We show behaves "well" general products, sense most products defined literature, product two by...

in this paper, the hyper - zagreb index of the cartesian product, composition and corona product of graphs are computed. these corrects some errors in g. h. shirdel et al.[11].

We consider the standard semi-direct product AoB of finite groups A,B. We show that with certain choices of generators for these three groups, the Cayley graph of A o B is (essentially) the zigzag product of the Cayley graphs of A and B. Thus, using the results of [RVW00], the new Cayley graph is an expander if and only if its two components are. We develop some general ways of using this const...

A coloring of a graph G is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees T1 and T2 equals min{∆(T1)+1, ∆(T2)+1}. We also prove that the acyclic chromatic number of direct product of two complete graphs Km and Kn is mn − m − 2, where m ≥ n ≥ 4. Several bounds for the acyclic chromatic numb...

let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...