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GROUP S<sub>3</sub> CORDIAL REMAINDER LABELING FOR PATH AND CYCLE RELATED GRAPHS
LOURDUSAMY, A.,WENCY, S. JENIFER,PATRICK, F. The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1
Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.
PEBBLING ON THE MIDDLE GRAPH OF A COMPLETE BINARY TREE
A. Lourdusamy,S. Saratha Nellainayaki,J. Jenifer Steffi 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.3
Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, ft(G), of a connected graph G, is the smallest positive integer such that from every placement of ft(G) pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than 2ft(G)-q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree M(Bh) and we show that the middle graph of a complete binary tree M(Bh) satisfies the 2t-pebbling property.
PEBBLING ON THE MIDDLE GRAPH OF A COMPLETE BINARY TREE
LOURDUSAMY, A.,NELLAINAYAKI, S. SARATHA,STEFFI, J. JENIFER The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.3
Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.
Group S_{3} Cordial Difference Labeling
A. Lourdusamy,S. Jenifer Wency,F. Patrick 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.3
Let h : V(G) \rightarrow S_{3} be a function defined in such a way that for every edge uv \in E(G), |o(h(u))-o(h(v))|=1. The function h is called a group S_{3} cordial difference labeling if |v_{h}(i) - v_{h}(j)| \leq 1 for every i, j \in S_{3}, i \neq j, where v_{h}(j) denote the number of vertices of G having label j under h. A graph G which admits a group S_{3} cordial difference labeling is called a group S_{3} cordial difference graph. In this paper, we introduce the concept of group S_{3} cordial difference labeling. We prove that path, cycle, bistar, comb, quadrilateral snake, ladder, gear and book are a group S_{3} cordial difference graphs.
COVERING COVER PEBBLING NUMBER OF A HYPERCUBE & DIAMETER d GRAPHS
A. Lourdusamy,Punitha Tharani 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.2
A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The covering cover pebbling number of a graph is the smallest number of pebbles, such that, however the pebbles are initially placed on the vertices of the graph, after a sequence of pebbling moves, the set of vertices with pebbles forms a covering of G. In this paper we find the covering cover pebbling number of n-cube and diameter two graphs. Finally we give an upperbound for the covering cover pebbling number of graphs of diameter d.
GROUP S<sub>3</sub> CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS
LOURDUSAMY, A.,WENCY, S. JENIFER,PATRICK, F. The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.3
Let G = (V (G), E(G)) be a graph and let g : V (G) → S<sub>3</sub> be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S<sub>3</sub> cordial remainder labeling of G if |v<sub>g</sub>(i)-v<sub>g</sub>(j)| ≤ 1 and |e<sub>g</sub>(1)-e<sub>g</sub>(0)| ≤ 1, where v<sub>g</sub>(j) denotes the number of vertices labeled with j and e<sub>g</sub>(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S<sub>3</sub> cordial remainder labeling is called a group S<sub>3</sub> cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S<sub>3</sub> cordial remainder labeling.
Group S_{3} Cordial Remainder Labeling of Subdivision of Graphs
A. Lourdusamy,S. Jenifer Wency,F. Patrick 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.3
Let G=(V(G),E(G)) be a graph and let g:V(G) → S_{3} be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S_{3} cordial remainder labeling of G if |v_{g}(i)-v_{g}(j)| ≤ 1 and |e_{g}(1)-e_{g}(0)| ≤ 1, where v_{g}(j) denotes the number of vertices labeled with j and e_{g}(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S_{3} cordial remainder labeling is called a group S_{3} cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S_{3} cordial remainder labeling.
SUPER VERTEX MEAN GRAPHS OF ORDER ≤ 7
A.Lourdusamy,Sherry George 한국전산응용수학회 2017 Journal of applied mathematics & informatics Vol.35 No.5
In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1, 2, 3, · · · , p + q} that induces for each vertex v the label defined by the rule fv(v) = Round, where Ev denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1, 2, 3, · · · , p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.
SUPER VERTEX MEAN GRAPHS OF ORDER ≤ 7
LOURDUSAMY, A.,GEORGE, SHERRY The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.5
In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.
GROUP S<sub>3</sub> MEAN CORDIAL LABELING FOR STAR RELATED GRAPHS
A. LOURDUSAMY,E. VERONISHA The Korean Society for Computational and Applied M 2023 Journal of applied mathematics & informatics Vol.41 No.2
Let G = (V, E) be a graph. Consider the group S<sub>3</sub>. Let g : V (G) → S<sub>3</sub> be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S<sub>3</sub> mean cordial labeling if |v<sub>g</sub>(i) - v<sub>g</sub>(j)| ≤ 1 and |e<sub>g</sub>(0) - e<sub>g</sub>(1)| ≤ 1, where vg(i) and e<sub>g</sub>(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S<sub>3</sub> mean cordial labeling is called group S<sub>3</sub> mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.