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Papers by Phaisatcha inpoonjai

Iranian Journal of Mathematical Sciences and Informatics, 2018

A graph is called supermagic if there is a labeling of edges where the edges are labeled with con... more A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.

Communications in Mathematics and Applications, 2021

A graph \(G\) is called supermagic if it admits a labelling of the edges by pairwise different co... more A graph \(G\) is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. A graph \(G\) is called degree-magic if it admits a labelling of the edges by integers \(1,2,\ldots,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). In this paper, some constructions of degree-magic labellings of some graphs obtained by generalizing the double graph of the disjoint union of a graph are presented. As a result, some supermagic graphs are obtained.

Journal of Mathematical and Computational Science, 2021

A graph G is called degree-magic if it admits a labelling of the edges by integers 1, 2, ..., |E(... more A graph G is called degree-magic if it admits a labelling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, a new construction of balanced degree-magic graphs is introduced.

Journal of Mathematical and Computational Science, 2021

An edge product cordial labelling is a variant of the well-known cordial labelling. In this paper... more An edge product cordial labelling is a variant of the well-known cordial labelling. In this paper, a balanced edge product cordial labelling is suggested and some sufficient conditions for balanced edge product cordial graphs are proved. Also, a construction of balanced edge product cordial graphs is presented.

Third International Conference on Advances in Applied Science and Environmental Engineering - ASEE 2015, Apr 12, 2015

Magic rectangles are a classical generalization of the well-known magic squares, and they are rel... more Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there is a labelling of the edges by integers 1, 2, ..., | () | EG such that the sum of the labels of the edges incident with any vertex v is equal to (1 | () |)deg() / 2. E G v  In this paper we generalize magic rectangles to be n-tuple magic rectangles, and prove the necessary and sufficient conditions for the existence of even ntuple magic rectangles. Using this existence we identify the sufficient condition for degree-magic labellings of the n-fold selfunion of complete bipartite graphs to exist.

Communications in Mathematics and Applications, 2019

A graph is called supermagic if there is a labeling of edges, where all edges are differently lab... more A graph is called supermagic if there is a labeling of edges, where all edges are differently labeled with consecutive positive integers such that the sum of the labels of all edges, which are incident to each vertex of this graph, is a constant. A graph G is called degree-magic if all edges can be labeled by integers 1, 2,. .. , |E(G)| so that the sum of the labels of the edges which are incident to any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, the necessary and sufficient conditions for the existence of degree-magic labelings of graphs obtained by taking the join and composition of complete tripartite graphs are found.

Indian Journal of Science and Technology, 2015

A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\S is adjacent t... more A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in S, and S is a total dominating set of G if every vertex of G is adjacent to at least one vertex of S. An ordered set W of vertices of a connected graph G is a locating set for G if distinct vertices have distinct codes with respect to W. In this paper, we study the domination and location in the multiplication of a graph. We find the necessary and sufficient conditions for the dominating and locating sets in the multiplication of a graph to exist. We also determine bounds or the exact domination and location numbers of this graph.

Magic rectangles are a classical generalization of the well-known magic squares, and they are rel... more Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph \(G\) is called degree-magic if there exists a labelling of the edges by integers \(1,2,\dots,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). Degree-magic graphs extend supermagic regular graphs. In this paper, we present a general proof of the necessary and sufficient conditions for the existence of degree-magic labellings of the \(n\)-fold self-union of complete bipartite graphs. We apply this existence to construct supermagic regular graphs and to identify the sufficient condition for even \(n\)-tuple magic rectangles to exist.

Iranian Journal of Mathematical Sciences and Informatics, 2018

A graph is called supermagic if there is a labeling of edges where the edges are labeled with con... more A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.

Communications in Mathematics and Applications, 2021

A graph \(G\) is called supermagic if it admits a labelling of the edges by pairwise different co... more A graph \(G\) is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. A graph \(G\) is called degree-magic if it admits a labelling of the edges by integers \(1,2,\ldots,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). In this paper, some constructions of degree-magic labellings of some graphs obtained by generalizing the double graph of the disjoint union of a graph are presented. As a result, some supermagic graphs are obtained.

Journal of Mathematical and Computational Science, 2021

A graph G is called degree-magic if it admits a labelling of the edges by integers 1, 2, ..., |E(... more A graph G is called degree-magic if it admits a labelling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, a new construction of balanced degree-magic graphs is introduced.

Journal of Mathematical and Computational Science, 2021

An edge product cordial labelling is a variant of the well-known cordial labelling. In this paper... more An edge product cordial labelling is a variant of the well-known cordial labelling. In this paper, a balanced edge product cordial labelling is suggested and some sufficient conditions for balanced edge product cordial graphs are proved. Also, a construction of balanced edge product cordial graphs is presented.

Third International Conference on Advances in Applied Science and Environmental Engineering - ASEE 2015, Apr 12, 2015

Magic rectangles are a classical generalization of the well-known magic squares, and they are rel... more Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there is a labelling of the edges by integers 1, 2, ..., | () | EG such that the sum of the labels of the edges incident with any vertex v is equal to (1 | () |)deg() / 2. E G v  In this paper we generalize magic rectangles to be n-tuple magic rectangles, and prove the necessary and sufficient conditions for the existence of even ntuple magic rectangles. Using this existence we identify the sufficient condition for degree-magic labellings of the n-fold selfunion of complete bipartite graphs to exist.

Communications in Mathematics and Applications, 2019

A graph is called supermagic if there is a labeling of edges, where all edges are differently lab... more A graph is called supermagic if there is a labeling of edges, where all edges are differently labeled with consecutive positive integers such that the sum of the labels of all edges, which are incident to each vertex of this graph, is a constant. A graph G is called degree-magic if all edges can be labeled by integers 1, 2,. .. , |E(G)| so that the sum of the labels of the edges which are incident to any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, the necessary and sufficient conditions for the existence of degree-magic labelings of graphs obtained by taking the join and composition of complete tripartite graphs are found.

Indian Journal of Science and Technology, 2015

A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\S is adjacent t... more A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in S, and S is a total dominating set of G if every vertex of G is adjacent to at least one vertex of S. An ordered set W of vertices of a connected graph G is a locating set for G if distinct vertices have distinct codes with respect to W. In this paper, we study the domination and location in the multiplication of a graph. We find the necessary and sufficient conditions for the dominating and locating sets in the multiplication of a graph to exist. We also determine bounds or the exact domination and location numbers of this graph.

Magic rectangles are a classical generalization of the well-known magic squares, and they are rel... more Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph \(G\) is called degree-magic if there exists a labelling of the edges by integers \(1,2,\dots,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \((1+|E(G)|)\deg(v)/2\). Degree-magic graphs extend supermagic regular graphs. In this paper, we present a general proof of the necessary and sufficient conditions for the existence of degree-magic labellings of the \(n\)-fold self-union of complete bipartite graphs. We apply this existence to construct supermagic regular graphs and to identify the sufficient condition for even \(n\)-tuple magic rectangles to exist.