Let P1, . . . , Pk be k vertex disjoint paths in a graph G where the ends of Pi are xi, and yi. Let H be the subgraph induced by the vertex sets of the paths. We find edge bounds E1(n), E2(n) such that, 1. If e(H) ≥ E1(|V (H)|), then there exist disjoint paths P ′ 1, . . . , P ′ k where the ends of P ′ i are xi and yi such that | S

The Satisfactory Bisection problem means to decide whether a given graph has a partition of its vertex set into two parts of the same cardinality such that each vertex has at least as many neighbors in its part as in the other part. A related variant of this problem, called Co-Satisfactory Bisection, requires that each vertex has at most as many neighbors in its part as in the other part. A ver...

BACKGROUND Hyperdynamic circulation due to reduced peripheral vascular resistance and increased cardiac output, and the development of portal hypertension are the hemodynamic changes observed in patients with liver cirrhosis. Such hemodynamic abnormalities appear in patients with late stage liver cirrhosis. Therefore, hemodynamic indices, which represent hyperdynamic circulation and portal hype...

Let P1, P2 be graph properties. A vertex (P1,P2)-partition of a graph G is a partition {V1, V2} of V (G) such that for i = 1, 2 the induced subgraph G[Vi] has the property Pi. A property R = P1◦P2 is defined to be the set of all graphs having a vertex (P1,P2)-partition. A graph G ∈ P1◦P2 is said to be uniquely (P1,P2)-partitionable if G has exactly one vertex (P1,P2)-partition. In this note, we...

PURPOSE The goal of the present study was to establish new Doppler reference ranges for maternal heart rate, intensity-weighted mean blood flow velocities (Vmean) and impedance indices (PI, RI) for the uterine artery by automated waveform analysis. MATERIALS AND METHODS A cross-sectional prospective study of 921 low-risk pregnancies was performed at 18 - 42 weeks of gestation. Uterine blood f...

Let G be a simple graph with the vertex set V(G) and edge set E(G) respectively. The degree of a vertex v in G is the number of vertices in G which are connected to v by an edge and denoted by dG(v). A topological index is a graph invarient which is numerical parameter obtained from a graph which characterize its topology.Thus for two isomorphic graphG and H the value of a particular topologica...

For a nontrivial graph G, its first Zagreb coindex is defined as the sum of degree sum over all non-adjacent vertex pairs in G and the second Zagreb coindex is defined as the sum of degree product over all non-adjacent vertex pairs in G. Till now, established results concerning Zagreb coindices are mainly related to composite graphs and extremal values of some special graphs. The existing liter...

BACKGROUND Among numerous modalities applied for evaluation of kidney diseases, Doppler ultrasonography (DU) provides information about the hemodynamic status of the kidneys. Meanwhile, the variability in DU parameters of the right and left kidney is a matter of controversy. The aim of this study was to determine whether any difference exists between the DU indices of the right and left kidney....

in this paper pi, szeged and revised szeged indices of an infinite family of ipr fullereneswith exactly 60+12n carbon atoms are computed. a gap program is also presented that isuseful for our calculations.

The augmented eccentric connectivity index of a graph which is a generalization of eccentric connectivity index is defined as the summation of the quotients of the product of adjacent vertex degrees and eccentricity of the concerned vertex of a graph. In this paper we established some relationships between augmented eccentric connectivity index and several other graph invariants like number of ...