When fault occurs on cross-coupling autotransformer (AT) power supply traction network, the up-line and down-line feeder circuit breakers in the traction substation trip at the same time without selectivity, which leads to an extended power failure. Based on equivalent circuit and Kirchhoff’s current law, the feeder current characteristic in the substation, AT station and sectioning post when T–R fault, F–R fault, and T–F fault occur are analyzed and their expressions are obtained. When the traction power supply system is equipped with wide-area protection measurement and control system, the feeder protection device in each station collects the feeder currents in other two stations through the wide-area protection channel and a wide-area current differential protection scheme based on the feeder current characteristic is proposed. When a short-circuit fault occurs in the power supply arm, all the feeder protection devices in each station receive the feeder currents with time stamp in other two stations. After data synchronous processing and logic judgment, the fault line of the power supply arm can be identified and isolated quickly. The simulation result based on MATLAB/Simulink shows that the power supply arm protection scheme based on wide-area current differential has good fault discrimination ability under different fault positions, transition resistances, and fault types. The verification of measured data shows that the novel protection scheme will not be affected by the special working conditions of the electrical multiple unit (EMU), and reliability, selectivity, and rapidity of relay protection are all improved.

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In this paper, we investigate the existence of [a, b]-factors with inclusion/exclusion properties under the toughness condition. We prove that if an incomplete graph G satisfies t(G) (a − 1) + a b and a, b are two integers with b > a > 1, then for any two given edges e 1 and e 2 , there exist an [a, b]-factor including e 1 , e 2 ; and an [a, b]-factor including e 1 and excluding e 2 ; as well as an [a, b]-factor excluding e 1 , e 2 unless e 1 and e 2 have a common end in the case of a = 2. For complete graphs, we obtain a similar result.

a b s t r a c tLet G H and G H denote the strong and Cartesian products of graphs G and H, respectively. In this note, we investigate the graph minor in products of graphs. In particular, we show that, for any simple connected graph G, the graph G K 2 is a minor of the graph G Q r by a construction method, where Q r is an r-cube and r = χ (G). This generalizes an earlier result of Kotlov [2].

Strong product G 1 G 2 of two graphs G 1 and G 2 has a vertex set V (G 1 ) × V (G 2 ) and two vertices (u 1 , v 1 ) and (u 2 , v 2 ) are adjacent whenever u 1 = u 2 and v 1 is adjacent to v 2 or u 1 is adjacent to u 2 and v 1 = v 2 , or u 1 is adjacent to u 2 and v 1 is adjacent to v 2 . We investigate the factor-criticality of G 1 G 2 and obtain the following. Let G 1 and G 2 be connected m-factor-critical and n-factor-critical graphs, respectively. Then(iv) if |V (G 1 )| 2m + 3 and |V (G 2 )| 2n + 3, then G 1 G 2 is (mn − min{[3m/2] 2 , [3n/2] 2 })-factor-critical.