Total Magic Cordial and Total Sequential Cordial Labeling of Path Related Graph - R. Parameswari (Innovations in Science and Technology Vol. 5, 2022)
A graph is simple and undirected and it is defined as G(V,E) with V as vertex set and E as edge set. Path graph is a simple graph whose vertices and edges are denoted as v1,v2,...vn and edges are vivi+1 with n number of vertices and n-1 number of edges. This chapter is discussing the cordial related labeling for special class of path graph called Square graph of path and Shadow graph of path. A graph G is said to have Total Sequential Cordial labeling, if there exists a mapping f : V U E\(rightarrow \) 0,1 such that for each (a,b) \(\) E,f (a,b) =|f(a) - f(b)|, provided the condition |f(0) - f(1)|\(≤\)1 hold, where f(0) = vf (0) + ef (0) and f(1) = vf (1) + ef (1) and vf (1), ef (1),i \(\) 0,1 are respectively, the number of vertices and edges labeled with i. Total magic cordial labeling is defined as ,if there exists a mapping f : V U E\(rightarrow \) 0,1 such that f(a) + f (b) + f(ab) = Cmod2 for all (a,b) \(\) E provided the condition |f(0) - f(1)| \(≤\) 1 is hold, where f(0) = vf (0) + ef (0) and f(1) = vf (1) + ef (1) and vf (i), ef (i),i \(\) 0,1 are respectively, the number of vertices and edges labeled with i.