In this paper, we continue the study of the enumeration problems of labeled graphs with k cycles that Tomscu didn't solve. A counting formula for the connected graphs with n labeled vertices and k cycles intersect...In this paper, we continue the study of the enumeration problems of labeled graphs with k cycles that Tomscu didn't solve. A counting formula for the connected graphs with n labeled vertices and k cycles intersecting at a point is given. As an application, together with Tomscu's result we solve the enumeration problem of labeled connected graphs with two cycles.展开更多
文摘In this paper, we continue the study of the enumeration problems of labeled graphs with k cycles that Tomscu didn't solve. A counting formula for the connected graphs with n labeled vertices and k cycles intersecting at a point is given. As an application, together with Tomscu's result we solve the enumeration problem of labeled connected graphs with two cycles.