a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph Kn is defined as 1 − n, and the rupture degree for an incomplete connected graph G is defined by r(G) = max{ω(G − X)− |X| − m(G − X) : X ⊂ V(G),ω(G − X) > 1}, where ω(G − X) is the number of components of G − X and m(G − X) is the order of a largest component of G − X . It is shown that this paramete...

Let be a graph. If  , G V E    is a function from the vertex set   V G to the set of positive integers. Then two vertices are   G , u v V   -equitable if     1 u v     . By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equ...

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

the first zagreb index, $m_1(g)$, and second zagreb index, $m_2(g)$, of the graph $g$ is defined as $m_{1}(g)=sum_{vin v(g)}d^{2}(v)$ and $m_{2}(g)=sum_{e=uvin e(g)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. in this paper, the firstand second maximum values of the first and second zagreb indicesin the class of all $n-$vertex tetracyclic graphs are presented.