# Search results for: Saieed Akbari

Journal of Graph Theory > 90 > 2 > 150 - 159

*G*be a 2

*k*‐edge‐connected graph with $k\ge 0$ and let $L\left(v\right)\subseteq \{k,\dots ,{d}_{G}\left(v\right)\}$ for every $v\in V\left(G\right)$. A spanning subgraph

*F*of

*G*is called an

*L*‐

*factor*, if ${d}_{F}\left(v\right)\in L\left(v\right)$ for every $v\in V\left(G\right)$. In this article, we show that if $\left|L\left(v\right)\right|\ge \lceil \frac{{d}_{G}\left(v\right)}{2}\rceil +1$ for every $v\in V\left(G\right)$, then

*G*has a

*k*‐edge‐connected

*L*‐factor. We also show that if $k\ge 1$ and $L\left(v\right)=\{\lfloor \frac{{d}_{G}\left(v\right)}{2}\rfloor ,\dots ,\lceil \frac{{d}_{G}\left(v\right)}{2}\rceil +k\}$ for every $v\in V\left(G\right)$, then

*G*has a

*k*‐edge‐connected

*L*‐factor.

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 75-82

Journal of Graph Theory > 87 > 1 > 35 - 45

*K*

_{4}and

*K*

_{3, 3}. We extend this result by showing that for an odd positive integer

*r*, if

*G*is a connected equimatchable

*r*‐regular graph, then $G\in \{{K}_{r+1},{K}_{r,r}\}$. Also it is proved that for an even

*r*, a connected triangle‐free...

Discussiones Mathematicae Graph Theory > 2017 > 37 > 3 > 835-840

Graphs and Combinatorics > 2017 > 33 > 4 > 595-615

*G*be a graph whose each component has order at least 3. Let $$s : E(G) \rightarrow {\mathbb {Z}}_k$$ s : E ( G ) → Z k for some integer $$k\ge 2$$ k ≥ 2 be an improper edge coloring of

*G*(where adjacent edges may be assigned the same color). If the induced vertex coloring $$c : V (G) \rightarrow {\mathbb {Z}}_k$$ c : V ( G ) → Z k defined by $$c(v)...

Linear Algebra and its Applications > 2017 > 517 > C > 1-10

Graphs and Combinatorics > 2015 > 31 > 3 > 497-506

Linear Algebra and Its Applications > 2014 > 445 > Complete > 18-28

Electronic Notes in Discrete Mathematics > 2014 > 45 > Complete > 23-27

Czechoslovak Mathematical Journal > 2014 > 64 > 2 > 433-446

*G*be a graph, and λ the smallest integer for which

*G*has a nowherezero λ-flow, i.e., an integer λ for which

*G*admits a nowhere-zero λ-flow, but it does not admit a (λ − 1)-flow. We denote the minimum flow number of

*G*by Λ(

*G*). In this paper we show that if

*G*and

*H*are two arbitrary graphs and

*G*has no isolated vertex, then Λ(

*G*∨

*H*) ⩽ 3 except two cases: (i) One of the graphs

*G*and

*H*is

*K*

_{2}and...

Graphs and Combinatorics > 2014 > 30 > 4 > 821-826

*F*of a graph

*G*is called an $${\mathcal{S}}$$ -factor of

*G*if $${\deg_F(x) \in \mathcal{S}}$$ for all vertices

*x*of

*G*, where deg

_{ F }(

*x*) denotes the degree of

*x*in

*F*. We prove the following theorem on {

*a*,

*b*}-factors of regular graphs. Let

*r*≥ 5 be an odd integer and

*k*be either an even integer such that 2 ≤

*k*<

*r*...

European Journal of Combinatorics > 2013 > 34 > 2 > 297-321

Algebras and Representation Theory > 2013 > 16 > 2 > 303-307

*R*be a ring with unity. The graph Γ(

*R*) is a graph with vertices as elements of

*R*, where two distinct vertices

*a*and

*b*are adjacent if and only if

*Ra*+

*Rb*=

*R*. Let Γ

_{2}(

*R*) be the subgraph of Γ(

*R*) induced by the non-unit elements of

*R*. Let

*R*be a commutative ring with unity and let

*J*(

*R*) denote the Jacobson radical of

*R*. If

*R*is not a local ring, then it was proved that: (a) If $\Gamma_2(R)\backslash...

Graphs and Combinatorics > 2013 > 29 > 3 > 327-331

*Roman dominating function*on a graph

*G*= (

*V*(

*G*),

*E*(

*G*)) is a labelling $${f : V(G)\rightarrow \{0,1,2\}}$$ satisfying the condition that every vertex with label 0 has at least a neighbour with label 2. The

*Roman domination number*

*γ*

_{ R }(

*G*) of

*G*is the minimum of $${\sum_{v \in V(G)}{f(v)}}$$ over all such functions. The

*Roman bondage number*

*b*

_{ R }(

*G*) of

*G*is the minimum cardinality of all...

Discrete Mathematics > 2012 > 312 > 10 > 1633-1637

European Journal of Combinatorics > 2010 > 31 > 7 > 1714-1724

Journal of Algebraic Combinatorics > 2010 > 32 > 3 > 459-464

*G*be a graph of order

*n*such that $\sum_{i=0}^{n}(-1)^{i}a_{i}\lambda^{n-i}$ and $\sum_{i=0}^{n}(-1)^{i}b_{i}\lambda^{n-i}$ are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of

*G*, respectively. We show that

*a*

_{i}≥

*b*

_{i}for

*i*=0,1,…,

*n*. As a consequence, we prove that for any

*α*, 0<

*α*≤1, if

*q*

_{1},…,

*q*

_{n}and

*μ*

_{1},…,

*μ*

_{n}are the signless Laplacian and the Laplacian...

Linear Algebra and Its Applications > 2009 > 430 > 8-9 > 2192-2199

Linear Algebra and Its Applications > 2008 > 429 > 11-12 > 2687-2690

Linear Algebra and Its Applications > 2007 > 422 > 1 > 341-347