Abstract In this study, we characterize the structure and some topological indices of a class random spider trees (RSTs) such as degree-based Gini index, Hoover generalized Zagreb other associated with these. We obtain exact asymptotic distributions number leaves via probabilistic methods. Moreover, relate model to RSTs that evolves in preferential attachment manner.

Recently, Hua et al. defined a new topological index based on degrees and inverse of distances between all pairs of vertices. They named this new graph invariant as reciprocal degree distance as 1 { , } ( ) ( ( ) ( ))[ ( , )] RDD(G) = u v V G d u  d v d u v , where the d(u,v) denotes the distance between vertices u and v. In this paper, we compute this topological index for Grassmann graphs.

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

Topological indices are of incredible significance in the field graph theory. Convex polytopes play a significant role both various branches mathematics and also applied areas, most notably linear programming. We have calculated some topological such as atom-bond connectivity index, geometric arithmetic K-Banhatti indices, K-hyper-Banhatti modified from families convex through M-polynomials. Th...

The Narumi–Katayama index of a graph G is equal to the product of the degrees of the vertices of G. In this paper we consider a new version of the Narumi– Katayama index in which each vertex degree d is multiplied d times. We characterize the graphs extremal w.r.t. this new topological index.

The energy spectrum of cosmic rays with primary energies between 10 14 eV and 10 16 eV has been studied with the CASA-MIA air shower array. The measured diierential energy spectrum is a power law (dj=dE / E ?) with spectral indices of 2:66 0:02 below approximately 10 15 eV and 3:00 0:05 above. A new method is used for measuring primary energy derived from ground based data in a compositionally ...