The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

The graphs having the maximum value of certain bond incident degree indices (including second Zagreb index, general sum-connectivity and zeroth-order Randi? index) in class all connected with fixed order number pendent vertices are characterized this paper. problem finding minimum values index from aforementioned is also addressed. One obtained results about first has already been proved papers...

let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2,cdots, n$. inspired by the randi'c matrix and the general randi'cindex of a graph, we introduce the concept of general randi'cmatrix $textbf{r}_alpha$ of $g$, which is defined by$(textbf{r}_alpha)_{i,j}=(d_id_j)^alpha$ if $v_i$ and $v_j$ areadjacent, and zero otherwise. s...

Let G = (V, E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... dn, di d(vi) sequence vertex degrees G. The general zeroth-order Randic index is defined as 0R?(G) ?ni =1 d?i, where an arbitrary real number. corresponding coindex via 0R??(G) ?ni=1(n?1?di)d?i. Some new bounds for the relationship between 0R??(G?) 0R???1(G?) ...

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...