Document Type : Primary Research paper
Department of Mathematics, Government Arts and Science College, Sivakasi, India.
The 𝑭-average eccentric graph 𝑨𝑬𝑭(𝑮) of a graph 𝑮 has the vertex set as in 𝑮 and any two vertices 𝒖 and 𝒗 are adjacent in 𝑨𝑬𝑭(𝑮) if either they are at a distance ⌊𝒆(𝒖)+𝒆(𝒗)𝟐⌋ while 𝑮 is connected or they belong to different components while 𝑮 is disconnected. A graph 𝑮 is called a 𝑭-average eccentric graph if 𝑨𝑬𝑭(𝑯)≅𝑮 for some graph 𝑯. In this paper, we find some sufficient conditions for a disconnected graph to be or not to be a 𝑭-average eccentric graph.