The total geo chromatic number of a graph
S. Annie Ajila, J. R. V. Edward · Malaya Journal of Matematik · 2020
A total geo chromatic set of a graph \(G\) is a geo chromatic set \(S_c\) such that the subgraph induced by \(S_c\) has no isolated vertices. The minimum cardinality of a total geo chromatic set of \(G\) is the total geo chromatic number of \(G\) and is denoted by \(\chi_{t g}(G)\). A total geo chromatic set of cardinality \(\chi_{t g}(G)\) is called a \(\chi_{t g}\)-set of \(G\). The total geo chromatic number of some standard graphs are determined and some general properties satisfied by this concept are studied.