in this paper we present explicit formulas for the eccentric connectivity index of three classesof chain hexagonal cacti. further, it is shown that the extremal chain hexagonal cacti withrespect to the eccentric connectivity index belong to one of the considered types. some openproblems and possible directions of further research are mentioned in the concluding section.

Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.

In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.

the sadhana index (sd) is a newly introduced cyclic index. efficient formulae for calculatingthe sd (sadhana) index of linear phenylenes are given and a simple relation is establishedbetween the sd index of phenylenes and of the corresponding hexagonal sequences.

In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.

The distance between two vertices u and v in a connected graph G is the number of edges lying shortest path (geodesic) them. A vertex x performs metric identification for pair (u, v) if only equality distances with implies that = (That is, different from x). minimum performing every defines dimension G. In this paper, we perform types polygonal cacti: chain cactus star cactus.

The objective of this study was to evaluate the best level of inclusion of cactus pear in the ensiling of elephant grass Brazil seeds (BRS) capiaçu (Pennisetum purpureum), its effects on fermentative characteristics; and nutritional value. Experimental treatments consisted of BRS capiaçu grass silage with five levels of inclusion of cactus pear (0, 5, 10, 15 and 20% inclusion as fresh ...

The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an n-hexagonal chain. Wiener number of an n x m hexagonal rectangle was found by the authors. An n x m hexagonal jagged-rectangle whose shape forms a rectangle and the number of hexagonal cells in each chain alternate between n and n 1...

The Wiener number of a molecular graph, or more generally of a connected graph, is equal to the sum of distances between all pairs of its vertices. A graph formed by a hexagon in the centre, surrounded by n rings of hexagonal cells, is called an n-Hexagonal net. A graph formed by a series of n hexagonal cells is called an n-Hexagonal chain. The purpose of this paper is to obtain the Wiener numb...

Double hexagonal chains” can be considered as benzenoids constructed by successive fusions of successive naphthalenes along a zig-zag sequence of triples of edges as appear on opposite sides of each naphthalene unit. In this paper, we discuss the numbers of k-matchings and k-independent sets of double hexagonal chains, as well as Hosoya indices and Merrifield–Simmons indices, and obtain some ex...