The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ (G) +2 colors. In this paper, the trueness of this co...The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ (G) +2 colors. In this paper, the trueness of this conjecture for complete k partite graph was proved, and the incidence chromatic number of complete k partite graphs was calculated.展开更多
The COVID-19 pandemic is strongly affecting many aspects of human life and society around the world.To investigate whether this pandemic also influences crime,the differences in crime incidents numbers before and duri...The COVID-19 pandemic is strongly affecting many aspects of human life and society around the world.To investigate whether this pandemic also influences crime,the differences in crime incidents numbers before and during the pandemic in four large cities(namely Washington DC,Chicago,New York City and Los Angeles)are investigated.Moreover,the Granger causal relationships between crime incident numbers and new cases of COVID-19 are also examined.Based on that,new cases of COVID-19 with significant Granger causal correlations are used to improve the crime prediction performance.The results show that crime is generally impacted by the COVID-19 pandemic,but it varies in different cities and with different crime types.Most types of crimes have seen fewer incidents numbers during the pandemic than before.Several Granger causal correlations are found between the COVID-19 cases and crime incidents in these cities.More specifically,crime incidents numbers of theft in Washington DC,Chicago and New York City,fraud in Washington DC and Los Angeles,assault in Chicago and New York City,and robbery in Los Angeles and New York City,are significantly Granger caused by the new case of COVID-19.These results may be partially explained by the Routine Activity theory and Opportunity theory that people may prefer to stay at home to avoid being infected with COVID-19 during the pandemic,giving fewer chances for crimes.In addition,involving new cases of COVID-19 as a variable can slightly improve the performance of crime prediction in terms of some specific types of crime.This study is expected to obtain deeper insights into the relationships between the pandemic and crime in different cities,and to provide new attempts for crime prediction during the pandemic.展开更多
An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence ...An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.展开更多
文摘The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey. They conjectured that every graph G can be incidence colored with Δ (G) +2 colors. In this paper, the trueness of this conjecture for complete k partite graph was proved, and the incidence chromatic number of complete k partite graphs was calculated.
文摘The COVID-19 pandemic is strongly affecting many aspects of human life and society around the world.To investigate whether this pandemic also influences crime,the differences in crime incidents numbers before and during the pandemic in four large cities(namely Washington DC,Chicago,New York City and Los Angeles)are investigated.Moreover,the Granger causal relationships between crime incident numbers and new cases of COVID-19 are also examined.Based on that,new cases of COVID-19 with significant Granger causal correlations are used to improve the crime prediction performance.The results show that crime is generally impacted by the COVID-19 pandemic,but it varies in different cities and with different crime types.Most types of crimes have seen fewer incidents numbers during the pandemic than before.Several Granger causal correlations are found between the COVID-19 cases and crime incidents in these cities.More specifically,crime incidents numbers of theft in Washington DC,Chicago and New York City,fraud in Washington DC and Los Angeles,assault in Chicago and New York City,and robbery in Los Angeles and New York City,are significantly Granger caused by the new case of COVID-19.These results may be partially explained by the Routine Activity theory and Opportunity theory that people may prefer to stay at home to avoid being infected with COVID-19 during the pandemic,giving fewer chances for crimes.In addition,involving new cases of COVID-19 as a variable can slightly improve the performance of crime prediction in terms of some specific types of crime.This study is expected to obtain deeper insights into the relationships between the pandemic and crime in different cities,and to provide new attempts for crime prediction during the pandemic.
基金Supported by the State Ethnic Affairs Commission of China (Grant No. 08XB07)
文摘An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.
