Given a connected graph G,the revised edge-revised Szeged index is defined as Sz_(e)^(*)(G)=∑_(e=uv∈E_(G))(m_(u)(e)+m_(0)(e)/2)(m_(v)(e)+m_(0)(e)/w),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G ly...Given a connected graph G,the revised edge-revised Szeged index is defined as Sz_(e)^(*)(G)=∑_(e=uv∈E_(G))(m_(u)(e)+m_(0)(e)/2)(m_(v)(e)+m_(0)(e)/w),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G lying closer to vertex u than to vertex u,the number of edges of G lying closer to vertex than to vertex u and the number of edges of G at the same distance to u and u,respectively.In this paper,by transformation and calculation,the lower bound of revised edge-Szeged index of unicyclic graphs with given diameter is obtained,and the extremal graph is depicted.展开更多
文摘Given a connected graph G,the revised edge-revised Szeged index is defined as Sz_(e)^(*)(G)=∑_(e=uv∈E_(G))(m_(u)(e)+m_(0)(e)/2)(m_(v)(e)+m_(0)(e)/w),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G lying closer to vertex u than to vertex u,the number of edges of G lying closer to vertex than to vertex u and the number of edges of G at the same distance to u and u,respectively.In this paper,by transformation and calculation,the lower bound of revised edge-Szeged index of unicyclic graphs with given diameter is obtained,and the extremal graph is depicted.
