on the first extended zeroth-order connectivity index of trees
نویسندگان
چکیده
the first extended zeroth-order connectivity index of a graph g is defined as 0 1/2 1 ( ) ( ) , v v v g g d where v (g) is the vertex set of g, and v d is the sum of degrees of neighbors of vertex v in g. we give a sharp lower bound for the first extended zeroth-order connectivity index of trees with given numbers of vertices and pendant vertices, and characterize the extremal trees. we also determine the n-vertex trees with the first three smallest first extended zeroth-order connectivity indices.
منابع مشابه
The eccentric connectivity index of bucket recursive trees
If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
متن کاملOn the second order first zagreb index
Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...
متن کاملAn Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
متن کاملA note on the zeroth-order general randić index of cacti and polyomino chains
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.
متن کاملOn the connectivity index of trees
The connectivity index χ1(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T (n, r) be the set of trees on n vertices with diameter r . In this paper, we determine all trees in T (n, r) with the largest and the second largest connectivity index. Also, the trees in T (n, r) with the largest and the second largest connecti...
متن کاملSufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
Let D be a digraph with vertex set V(D) .For vertex v 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 and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of science and technology (sciences)ISSN 1028-6276
دوره 38
شماره 3 2014
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023