Graphs whose sum of independent domination number and chromatic number equals to 2n-6 for any n>3

eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences December 2008 20 3 757 762 jusps-B 1401 article Graphs whose sum of independent domination number and chromatic number equals to 2n-6 for any n>3 G. MAHADEVAN (gmaha2003@yahoo.co.in) 1 A. SELVAM AVADAYAPPAN (selvam-avadayappan@yahoo.co.in) 2 M. AMRA PARVEEN (amra_imam@yahoo.co.in) 3 Department of Mathematics, Gandhigram Rural University, Gandhigram - 624302 (INDIA) Department of Mathematics, V.H.N.S.N., College, Virudhunagar - 626 001 (INDIA) Department of Mathematics, Gandhigram Rural Universiry, Gandhigram A subset S of V is called a dominating set in G, if every vertex in V- S is adjacent to at least one vertex in S. A Dominating set is said to be independent dominating set if the induced subgraph < V > is independent. The minimum cardinality taken over all, such independent dominating sets is called the independent domination number and is denoted by gi(G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number c(G). It was already proved that gi(G) + c(G) £ 2n-1 and corresponding extremal graphs were characterized of order up to 2n-5. In this paper we characterize the class of graphs for which gi(G)+c(G) = 2n-6 for any n > 3.   https://ultraphysicalsciences.org/paper/1401/ Independent Chromatic number domination