For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of n-vertex connected graphs with k cut vertices, the upper bound for M1and M2-values of n-vertex connected graphs with k cut vertices are deter...

INTRODUCTION We examined the best-fit index for describing the constitutional or physical characteristics of Sasang typology for its universal application. METHODS Ponderal index (PI), body mass index (BMI), and basal metabolic rate (BMR) of the nationwide participants (n = 1663; age, 31-60 years) were calculated. We described and analyzed the usefulness of each index for maximizing the diffe...

We investigate the virtual specialness of a compact cube complex X that splits as graph nonpositively curved complexes. prove when each vertex space has word-hyperbolic $$\pi _1$$ and _1X$$ “finite stature” relative to its edge groups. The results generalize motivating case tree $$\times $$ lattices are products.

Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic...

Resistance to Meloidogyne arenaria race 1 is not currently available in commercial peanut cultivars. Moderate levels of resistance have been identified in Arachis hypogaea plant introductions (PI) in previous greenhouse studies. The purpose of this work was to evaluate the effects of resistance in peanut PI on populations dynamics of M. arenaria in field plots. The PI designated as resistant in...