Let μ (G) and μmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and diameter D. If H is a proper subgraph of G, then μ (G) − μ (H) > 1 nD . (ii) If G is a connected regular nonbipartite graph of order n and diameter D, then μ (G) + μmin (G) > 1 nD .

Purpose: The main pulmonary artery diameter is an indirect indicator of vascular bed resistance. In this study, it was aimed to reveal which parameters are associated with respiratory distress by evaluating the affecting in cases COVID-19 pneumonia. Methods: relationship between comorbid diseases, clinical findings, laboratory values, infiltration features, and (MPAD) statistically evaluated. R...

In embolization procedures of the external carotid artery (ECA) system, it is ideal to selectively embolize only the involved feeding branch or branches. This usually requires superselective catheterization , which can be difficult. The catheter diameter may approximate vessel diameter closely enough to reduce flow. Vessel spasm may be generated by catheterization attempts. Spasm may lead to re...

carbon spheres were fabricated by hydrothermal method and their structural properties were investigated. carbon spheres with average sizes around of 230, 320 and 430 nm were synthesized in different concentration of glucose aqueous solution and different hydrothermal reaction time. the temperature of 180 °c by a hydrothermal reaction was fixed in all of glucose concentration and hydrothermal re...

the average distance of a vertex $v$ of a connected graph $g$is the arithmetic mean of the distances from $v$ to allother vertices of $g$. the proximity $pi(g)$ and the remoteness $rho(g)$of $g$ are defined as the minimum and maximum averagedistance of the vertices of $g$. in this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore-like bound is attained in the case of diameter k = 3, and that bipartite mixed graphs of diameter k ≥ 4 do not exist.

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter d,(G), the (W 1 )-fault diameter D,,(G), and the w-Rabin number r,(G) have been used to measure network reliability and efficiency. In this paper, we study these parameters for an important class of parallel networks Butterfly networks. The main result of this paper is to d...

The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.

The alpaca is the most important fiber producer of the South American camelid species, and is an important source of income for the Andean communities. Nowadays, fiber diameter is considered the main selection objective in alpaca populations throughout the world. However, fiber diameter increases with the age of the animals, and it would be preferable to select those animals that maintain a thi...