On Chromatic Polynomials of Some Kinds of Graphs

Hao, Rong‐Xia; Liu, Yanpei

doi:10.1007/s10255-004-0164-0

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…Kano, Lu and Yu [12] presented a sufficient condition for the existence of P ≥3 -factor. Wu [15], Zhou et al [25,28,[31][32][33] derived some sufficient conditions for graphs to possess P ≥3 -factors with given properties. Gao, Wang and Chen [8] posed some tight bounds for the existence of P ≥3 -factors in graphs.…”

Section: Theorem 1 ( [14]mentioning

confidence: 99%

International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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Ultra-dense networks are widely regarded as a promising solution to explosively growing applications of Internet-of-Things (IoT) mobile devices (IMDs). However, complicated and severe interferences need to be tackled properly in such networks. To this end, both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are utilized at first. Then, in order to attain a goal of green and secure computation offloading, under the proportional allocation of computational resources and the constraints of latency and security cost, joint device association, channel selection, security service assignment, power control and computation offloading are done for minimizing the overall energy consumed by all IMDs. It is noteworthy that multi-step computation offloading is concentrated to balance the network loads and utilize computing resources fully. Since the finally formulated problem is in a nonlinear mixed-integer form, it may be very difficult to find its closed-form solution. To solve it, an improved whale optimization algorithm (IWOA) is designed. As for this algorithm, the convergence, computational complexity and parallel implementation are analyzed in detail. Simulation results show that the designed algorithm may achieve lower energy consumption than other existing algorithms under the constraints of latency and security cost.

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Section: Theorem 1 ( [14]mentioning

confidence: 99%

International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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“…In [1], Shubo Chen has investigated absolute sum of chromatic polynomial coefficients of forest, q -tree, unicyclic graphs and quasi wheel graphs. In [2], Rong-xia Hao et al have proposed a new method to calculate the chromatic polynomial of the complements of a wheel and a fan graph. In [3], Matthias Beck et al have developed and executed a computer program that efficiently determines the number of proper k-colorings for a given signed graph.…”

Section: Introductionmentioning

confidence: 99%