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Binding numbers and fractional $(g,f,n)$-critical graphs
Sizhong Zhou,Zhiren Sun 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
Let $G$ be a graph, and let $g,f$ be two nonnegative integer-valued functions defined on $V(G)$ with $g(x)\leq f(x)$ for each $x\in V(G)$. A graph $G$ is called a fractional $(g,f,n)$-critical graph if after deleting any $n$ vertices of $G$ the remaining graph of $G$ admits a fractional $(g,f)$-factor. In this paper, we obtain a binding number condition for a graph to be a fractional $(g,f,n)$-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional $(f,n)$-critical graphs, Inform. Process. Lett. 109(2009)811--815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.
REMARKS ON NEIGHBORHOODS OF INDEPENDENT SETS AND (a, b, k)-CRITICAL GRAPHS
Sizhong Zhou,Zhiren Sun,Lan Xu 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.5
Let a and b be two even integers with 2 ≤ a < b, and let k be a nonnegative integer. Let G be a graph of order n with n ≥(a+b-1)(a+b-2)+bk-2 b . A graph G is called an (a, b, k)-critical graph if afterdeleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, it is proved that G is an (a, b, k)-critical graph if |NG(X)| >(a - 1)n + |X| + bk - 2a + b - 1 for every non-empty independent subset X of V (G), and δ(G) >(a -1)n + a + b + bk - 3a + b - 1. Furthermore, it is shown that the result in this paper is best possible insome sense.
REMARKS ON NEIGHBORHOODS OF INDEPENDENT SETS AND (a, b, k)-CRITICAL GRAPHS
Zhou, Sizhong,Sun, Zhiren,Xu, Lan The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.5
Let $a$ and $b$ be two even integers with $2{\leq}a<b$, and let k be a nonnegative integer. Let G be a graph of order $n$ with $n{\geq}\frac{(a+b-1)(a+b-2)+bk-2}{b}$. A graph G is called an ($a,b,k$)-critical graph if after deleting any $k$ vertices of G the remaining graph of G has an [$a,b$]-factor. In this paper, it is proved that G is an ($a,b,k$)-critical graph if $${\mid}N_G(X){\mid}>\frac{(a-1)n+{\mid}X{\mid}+bk-2}{a+b-1}$$ for every non-empty independent subset X of V (G), and $${\delta}(G)>\frac{(a-1)n+a+b+bk-3}{a+b-1}$$. Furthermore, it is shown that the result in this paper is best possible in some sense.
BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS
ZHOU, SIZHONG,SUN, ZHIREN The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.
Dazhuan Wu,Leqin Wang,Zongrui Hao,Zhifeng Li,Zhiren Bao 대한기계학회 2010 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.24 No.2
An experimental study has been carried out in order to analyze the cavitation of a centrifugal pump and its effect on transient hydrodynamic performance during transient operation. The transient characteristics of the centrifugal pump were tested under various suction pressure and starting conditions. In transient operation of continuous starting and stopping process, instantaneous rotational speed, head,flow rate and suction pressure of the pump were measured. The effect of cavitation on transient performance of the centrifugal pump during transient operation was analyzed, and then the effects of starting acceleration rate and suction pressure of pump on cavitation were presented. Results showed that the cavitation would be delayed during rapid starting period. However, in the condition of low suction pressure and high rotational speed, pump cavitation is inescapable even if the starting period is less than a second. After the serious transient cavitation occurred, the transient performance of centrifugal pump would decline obviously, and the instantaneous head of pump would fluctuate.