Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images a...Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph F of G is a CI-graph if and only if all regular subgroups of Aut（F） isomorphic to G are conjugate in Aut（F）. A semi-Cayley graph （also called bi-Cayley graph by some authors） over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits （of equal size）. In this paper, we introduce the concept of SCI-graph （semi-Cayley isomorphism） and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs.展开更多
文摘Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph F of G is a CI-graph if and only if all regular subgroups of Aut（F） isomorphic to G are conjugate in Aut（F）. A semi-Cayley graph （also called bi-Cayley graph by some authors） over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits （of equal size）. In this paper, we introduce the concept of SCI-graph （semi-Cayley isomorphism） and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs.
