3-Difference cordial labeling of some path related graphs

Abstract

<p>Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k is an integer 2 ≤ k ≤ p. For each edge uv, assign the label |f(u) − f(v)|. f is called k-difference cordial labeling of G if |vf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x, ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternate triangular snake, alternate quadrilateral snake, irregular triangular snake, irregular quadrilateral snake, double triangular snake, double quadrilateral snake, double alternate triangular snake, and double alternate quadrilateral snake.</p>

3-Difference cordial labeling of some path related graphs

“…The irregular triangular snake IT n is obtained from the path u 1 u 2 ...u n with vertex set V (IT n ) = V (P n ) ∪ {v i : 1 ≤ i ≤ n − 2} and the edge set E(IT n ) = E(P n ) ∪ {u 5 by the integers 1, 3, 2, 1, 3. Then assign the labels 1, 3, 2, 1, 3 to the next five vertices 10 . Continuing this way, assign the label to the next five vertices and so on.…”

3-difference cordiality of some corona graphs

“…The notion of difference cordial labeling was introduced by R. Ponraj, S. Sathish Narayanan and R. Kala in [4]. Seoud and Salman [10], studied the difference cordial labeling behavior of some families of graphs and they are ladder, triangular ladder, grid, step ladder and two sided step ladder graphs etc. Recently Ponraj et al [4], introduced the concept of k-difference cordial labeling of graphs and studied the 3-difference cordial labeling behavior of star, m copies of star etc.…”

“…Recently Ponraj et al [4], introduced the concept of k-difference cordial labeling of graphs and studied the 3-difference cordial labeling behavior of star, m copies of star etc. In [5,6,7,8,9] they discussed the 3-difference cordial labeling behavior of path, cycle, complete graph, complete bipartite graph, star, bistar, comb, double comb, quadrilateral snake, wheel, helms, flower graph, sunflower graph, lotus inside a circle, closed helm, double wheel, union of graphs with the star, union of graphs with splitting graph of star, union of graphs with subdivided star, union of graphs with bistar,…”

Corona Graphs for Astronomical Calcualtions using L-Cordial Labeling

“…Initially L-Cordial Labeling (LCL) was introduced in [7] and proved some graphs for the same labeling in [8,9] LCL.In [2,3] et al proved cube Q 3 , octahedron and special graph admits LCL. H-Related graph for square difference, Prime cordial and Cube difference labeling were studied in [1, 6,14].In [15] Veena Shinde-Deorde, studied H-Cordial and prime labeling .In [10,11,12,13] Ponraj et.al proved snake graph and there corona admits difference cordial labeling. Detailed survey descriptions are given in [4].…”