منابع مشابه
Cacti with Extremal Pi Index
The vertex PI index PI(G) = ∑ xy∈E(G)[nxy(x) + nxy(y)] is a distance-based molecular structure descriptor, where nxy(x) denotes the number of vertices which are closer to the vertex x than to the vertex y and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947. A connected graph is a cactus if any two of its cycles have at most one common ver...
متن کاملOn the Randić index of cacti
The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti.
متن کاملOn the Harary Index of Cacti
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G (n, r) be the set of cacti of order n and with r cycles, ξ(2n, r) the set of cacti of order 2n with a perfect matching and r cycles. In this paper, we give the sharp upper bounds of t...
متن کاملOn the Estrada index of cacti
Let G be a simple connected graph on n vertices and λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = Σ i=1 ei . A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, ...
متن کاملOn generalized atom-bond connectivity index of cacti
The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABCa index for cacti of order $n$ ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2019
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1915865h