Study on total irregularity of graphs
M Sakthi Pandiyammal, V Mohana · Journal of Physics Conference Series · 2018
The total irregularity of a graph G is defined by For an ordered degree sequence of V (G) = { v 1 , v 2 , ..., v n } with d( v 1 ) ≤ d( v 2 ) ≤ ... ≤ d( v n ), irr t ( G ) can be expressed in the form where d G ( x ) is the degree of x ∈ V ( G ). An edge e∈E(G) is said to be total irregular positive (negative, stable) inner edge if irr t > irr t ( G ) (irr t ,irr t = irr t ( G ) respectively). Total irregular positive inner edge is denoted by TIPI edge. Similarly we use the notations TINI, TISI suitably. A graph G is called total irregular positive (negative, stable) inner graph if all the edges e∈ E ( G ) are total irregular positive (negative, stable) inner edges; otherwise G is called a total irregular mixed inner graph.Total irregular positive inner graph is denoted by TIPI graph. Similarly we use the notations TINI, TISI suitably. In this paper, we prove that the Complete graph K mn ,m ≠ n and m,n ≥ 2 is a TIPI graph and the Star graph S n n ≥ 3 is a TINI graph.