Total Magic Cordial and Total Sequential Cordial Labeling of Path Related Graph

Abstract

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) \(\in\) E,f (a,b) =|f(a) - f(b)|, provided the condition |f(0) - f(1)|\(\leq\)1 hold, where f(0) = vf (0) + ef (0) and f(1) = vf (1) + ef (1) and vf (1), ef (1),i \(\in\) {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) \(\in\) E provided the condition |f(0) - f(1)| \(\leq\) 1 is hold, where f(0) = vf (0) + ef (0) and f(1) = vf (1) + ef (1) and vf (i), ef (i),i \(\in\) {0,1} are respectively, the number of vertices and edges labeled with i.