Introduction/purpose: In the current literature, several dozens of vertex-degree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is (= sum absolute values eigenvalues) respective matrix. paper examines some general properties bipartite graphs. Results: Estimates (lower and upper bounds) established for graphs in which there no c...

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.

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...