Integral Root Labeling of Pm ∪ G Graphs

Let G=(V,E) be a graph with p vertices and q edges. Let f:V?{1,2,"¦q+1} is called an Integral Root labeling if it is possible to label all the vertices v?V with distinct elements from {1,2,"¦q+1} such that it induces an edge labeling f^+:E?{1,2,"¦q} defined as f^+ (uv)=?v((?(f(u))?^2+?(f(v))?^2+f(u)f(v))3)? is distinct for all uv?E. (i.e.) The distinct vertex labeling induces a distinct edge labeling on the graph. The graph which admits Integral Root labeling is called an Integral Root Graph. In this paper, we investigate the Integral Root labeling of P_m?G graphs likeP_m?P_n,P_m?(P_n ?K_1), P_m?L_n,P_m?(P_n ?K_1,2), P_m?(P_n ?K_1,3), P_m?(P_n ?K_1)?K_1,2 V. L. Stella Arputha Mary | N. Nanthini"Integral Root Labeling of Pm ∪ G Graphs" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18233.pdf http://www.ijtsrd.com/mathemetics/other/18233/integral-root-labeling-of-pm-∪-g-graphs/v-l-stella-arputha-mary