The Maximal Total Irregularity of Unicyclic Graphs

摘要

In [1], Hosam Abdo and Darko Dimitrov introduced the total irregularity of a graph. For a graph G, it is defined as <br>irr(t) (G) = 1/2 Sigma u,v is an element of V vertical bar d(G)(u) - d(G)(v)vertical bar, <br>where d(G) (u) denotes the vertex degree of a vertex u is an element of V (G). In this paper, we introduce two transformations to study the total irregularity of unicyclic graphs, and determine the graph with the maximal total irregularity among all unicyclic graphs with n vertices.

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