The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamilt...The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.展开更多
In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformat...In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.展开更多
文摘The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.
基金supported by the National Natural Science Foundation of China (10771095)the Guangxi Science Foundation(0832107,0991102)the Scientific Research Foundation of Guangxi Educational Committee (200707LX233)
基金Supported by National Natural Science Foundation(11161006)Guan-gxi Natural Science Foundation(2010GXNSFB013048,2011GXNSFA018139)Scientific Research Foundation of Guangxi Educational Committee(201012MS140)
文摘In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.
