YOKESH D
@aiht.ac.in
HOD MATHEMATICS
ANAND INSTITUTE OF HIGHER TECHNOLOGY
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics
Scopus Publications
Scopus Publications
D. Yokesh, G. Nirmala, and K. Anitha
IOP Publishing
Abstract Let G be a graph and let c:V(G)→{1,2…..k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code (v) = (a0, a1, a2….ak) where a0 is the color assigned to v and for 1 ⩽ i ⩽ k, ai is the number of the vertices of G adjacent to that are colored i. The coloring c is called recognizable if distinct vertices have distinct color codes and the recognition number of G is the minimum positive integer k for which G has a recognizable k-coloring. In this paper we introduced a new variation of above parameter namely distance-2 irregular coloring. We initiate a study of this parameter and also find the distance 2-irregular chromatic number of some standard graphs.
R. Avudainayaki and D. Yokesh
Union of Researchers of Macedonia
For a graph G and a proper coloring c : V (G) → {1, 2, 3, . . . , k} of the vertices of G for some positive integer k, the color code of a vertex v of G (with respect to c) is the ordered (k + 1)-tuple code(v) = (a0, a1, a2, . . . , ak) where a0 is the color assigned to v and 1 ≤ i ≤ k, ai is the number of vertices of G adjacent to v that are colored i. The coloring c is irregular if distinct vertices have distinct color codes and the irregular chromatic number χir(G) of G is the minimum positive integer k for which G has an irregular k-coloring. In this paper, we obtain the values of irregular coloring for SF (n, 1), friendship graph and splitting graph of star graph.
P. Roushini Leely Pushpam and D. Yokesh
Springer International Publishing
P. Roushini Leely Pushpam and D. Yokesh
Taru Publications
Abstract Let G = (V,E) be an arbitrary graph. For any subset X of V let B(X) be the set of all vertices in V – X that have a neigbor in a set X. J.L. Mashburn et al.,, defined the differential of a set X, to be ∂ (X) = | B(X) | − | X | and the differential of a graph ∂ (G) = max{∂ (X)}, for any subset X of V. The A-differential of a set X is defi ned as ∂ A (X) = | B(X) | − | A(X) | , where A(X) = X ⋂ N(X), the non isolates in < x >, the vertices in X having a neighbor in X. The A -differential of a graph is ∂ A (G) = max{∂A(X)}, for any subset X of V. For any graph G, it is observed that ∂ A (G) + 2γ t (G) ≥ n and ∂ A (G) + i (G) ≥ n, where γ t (G) is the total domination number of G and i (G) is the independent domination number of G. In this paper, we characterize certain classes of graphs for which ∂ A (G) + 2γ t (G) = n and ∂ A (G) + i (G) = n.
P. Roushini Leely Pushpam and D. Yokesh
Tamkang Journal of Mathematics
Let $X subset V$ be a set of vertices in a graph $G = (V, E)$. The boundary $B(X)$ of $X$ is defined to be the set of vertices in $V-X$ dominated by vertices in $X$, that is, $B(X) = (V-X) cap N(X)$. The differential $ partial(X)$ of $X$ equals the value $ partial(X) = |B(X)| - |X|$. The differential of a graph $G$ is defined as $ partial(G) = max { partial(X) | X subset V }$. It is easy to see that for any graph $G$ having vertices of maximum degree $ Delta(G)$, $ partial(G) geq Delta (G) -1$. In this paper we characterize the classes of unicyclic graphs, split graphs, grid graphs, $k$-regular graphs, for $k leq 4$, and bipartite graphs for which $ partial(G) = Delta(G)-1$. We also determine the value of $ partial(T)$ for any complete binary tree $T$.