On The Adjacent Vertex Strongly Distinguishing Total Coloring Of Some Classes Of Graphs

Graph coloring theory,as a hot topic in graph theory,has been widely concerned by scholars at home and abroad.In 2007,Zhongfu Zhang et al.proposed the concept of adjacent vertx strongly distinguishing total coloring of graphs based on channel allocation,co-frequency resonance problems in communication networks and adjacent vertex distinguishing total coloring of graphs.Let G=(V(G),E(G))be a simple connected graph with |V(G)|≥3,and k be a positive integer.If f is a mapping from V(G)∪ E(G)to {1,2,…,k} such that1)for any uv∈ E(G),f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv);2)for any adjacent edges uv,uw ∈ E(G)(v≠w),f(uv)≠f(uw);3)for any edge uv ∈ E(G),C_f<u>≠C_f<v>,where C_f...