In this paper chain cacti are considered. First, for two specific classes of chain cacti (orto-chains and meta-chains of cycles with h vertices) the recurrence relation for independence polynomial is derived. That recurrence relation is then used in deriving explicit expressions for independence number and number of maximum independent sets for such chains. Also, the recurrence relation for tot...

The cactus life-form is cited as an example of a tight relationship between organism form and function: a succulent, long-lived, photosynthetic stem allows cacti to survive long periods of drought while maintaining a positive tissue water status. Pereskia (Cactaceae) comprises 17 species of leafy shrubs and trees that are thought to represent the original cactus condition. Recent phylogenetic w...

A cactus is a connected graph in which any two cycles have at most one vertex in common. We determine the unique graphs with maximum signless Laplacian spectral radius in the class of cacti with given number of cycles (cut edges, respectively) as well as in the class of cacti with perfect matchings and given number of cycles.

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.

Four bacterial species isolated from the rhizoplane of cacti growing in bare lava rocks were assessed for growth promotion of giant cardon cactus seedlings (Pachycereus pringlei). These bacteria fixed N(2), dissolved P, weathered extrusive igneous rock, marble, and limestone, and significantly mobilized useful minerals, such as P, K, Mg, Mn, Fe, Cu, and Zn in rock minerals. Cardon cactus seeds ...

To compare the bacterial communities residing in necrotic tissues of columnar cacti of the Sonoran Desert, isolates from 39 organ pipe, 19 saguaro, and 16 senita cacti were obtained. The isolates were clustered into 28 conspecific groups on the basis of their fatty acid profiles. The distributions of the individual bacterial isolates varied among cactus species. Seven of the 28 species groups w...

In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles. Résumé. Dans cet article, nous construisons une bijection pour 3-cacti partitionnés faisant apparaı̂tre une nouvelle formule pour l’énumération des factorisations d’un long cycle en trois permutat...

A graceful labelling of a graph with n edges is a vertex labelling where the induced set of edge weights is {1, . . . , n}. A near graceful labelling is almost the same, the difference being that the edge weights are {1, 2, . . . , n − 1, n + 1}. In both cases, the weight of an edge is the absolute difference between its two vertex labels. Rosa [8] in 1988 conjectured that all triangular cacti ...