Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics
7
Scopus Publications
Scopus Publications
Eternal paired domination in graphs D. Yokesh, P. Roushini Leely Pushpam, G. Navamani Discrete Mathematics Algorithms and Applications, 2025 Eternal dominationof a graph requires the vertices of the graph to be protected, against infinitely long sequences of attacks, by guards located at vertices (at most one guard at each vertex), with the requirement that the configuration of guards induces a dominating set at all times. Two models of the problem, one in which only one guard moves at a time and one in which more than one guard may move simultaneously are studied in the literature. In this paper, we study the model in which more than one guard move simultaneously and where the configuration of guards induces a paired dominating set at all times.
Distance-2 Irregular chromatic numbers for some graphs D. Yokesh, G. Nirmala, K. Anitha Journal of Physics Conference Series, 2021 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.
Irregular coloring of some special graphs R. Avudainayaki, D. Yokesh Advances in Mathematics Scientific Journal, 2020 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.
Restrained differential of a graph P. Roushini Leely Pushpam, D. Yokesh Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2017
A-differentials and total domination in graphs P. Roushini Leely Pushpam, D. Yokesh Journal of Discrete Mathematical Sciences and Cryptography, 2013 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.
Differential coloring of graphs Sut Journal of Mathematics, 2011
Differentials in certain classes of graphs P. Roushini Leely Pushpam, D. Yokesh Tamkang Journal of Mathematics, 2010 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 $T$.
