The neighbour-integrity of total graphs

Let Gbe a graph. A vertex subversion strategy of G, say S, is a set of vertices in G whose closed neighbourhood is removed from G. The survival-subgraph is denoted by G/S. The neighbour-integrity of G NI(G), is defined to be , where S is any vertex subversion strategy of G, and c(G/S) is the maximum order of the components of G/S. This paper includes results on the neighbour-integrity of total graphs.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  Lowell W. Beineke,et al.  Edge-integrity: a survey , 1994, Discret. Math..

[3]  R. E. Pippert.  On the toughness of a graph , 1972 .

[4]  Margaret B. Cozzens,et al.  Edge-neighbor-integrity of trees , 1994, Australas. J Comb..

[5]  Wayne Goddard,et al.  A Survey of Integrity , 1992, Discret. Appl. Math..

[6]  Wayne Goddard,et al.  On the Toughness of a Graph , 1990 .

[7]  D. R. Woodall.  The binding number of a graph and its Anderson number , 1973 .

[8]  Margaret B. Cozzens,et al.  Vertex-neighbor-integrity of trees , 1996, Ars Comb..

[9]  Margaret B. Cozzens,et al.  Bounds of edge-neighbor-integrity of graphs , 1997, Australas. J Comb..