TOTAL DOMINATION NUMBER OF ROOTED PRODUCT GRAPH P_m⨀C_n

Abstract

Total domination number of a rooted product of a path and cycle P_m⨀C_n, when root vertex is included in total dominating set is m- times the total domination number of a cycle graph is expressed in terms of total domination number of cycle graph and the path length m.The total domination of a rooted product giving γ_t 〖(P〗_m⨀C_n)={█(mγ_t (C_n ) if n≡0( mod4) @γ_t 〖(P〗_m)+mγ_t (C_(n-1) ) if n≡1 (mod4)@m+mγ_t (C_(n-2) ) if n≡2 (mod4))┤