A triple vertex (TV) and triple vertex path (TVP) graph are defined as new concepts. These concepts consider the main point of this work to modify the symmetric encryption (SE) schemes and increase the security level in comparison with the previous ES schemes. In proposed ES schemes, the ciphertexts of the plaintexts are sent to the receiver entity as the TVP graph. Two study cases of the proposed TVPG-SE schemes are presented as new experimental results. The security issues of the proposed TVPG-SE schemes have been determined. The TVPG-SE schemes consider new insights for more secure communications.