VDGOOD Journal of Mathematics

Discussion about chromatic number, total number of vertex and edges in Mongolian Tent Graph M r, 3 R.Malathi Assistant Professor of Mathematics SCSVMV, Enathur, Kanchipuram, Tamilnadu, India malathilathar@gmail.com Abstract: In graph theory, a Mongolian tent graph is defined as the graph obtained by adding an extra vertex above the graph and joining some of the other vertex of the top row to the additional vertex. Researchers have been using this concept effectively to different types of graphs. In this paper, we are going to discuss about the chromatic number, total number of vertices and edges in M r, 3. Keywords: Vertex Labeling, Edge Labeling, Mongolian Tent Graph, chromatic number and degree of vertex & edges. AMS Subject Classification: 05C78, 05C99

Finding Maximum Independent set of Mongolian tent graph Mr, 3 R.Malathi Assistant Professor of Mathematics SCSVMV, Enathur, Kanchipuram, Tamilnadu, India malathilathar@gmail.com Abstract: In graph theory, a Mongolian tent graph is defined as the graph obtained by adding an extra vertex above the graph and joining some of the other vertex of the top row to the additional vertex. Researchers have been using this concept effectively to different types of graphs. In this paper, we find out the Maximum Independent Set in a Mongolian tent graph. AMS Subject Classification: 05C15, 05C69, 05C99 Key Words: Adjacent, Independent set, Maximum Independent set

Finding Laplacian Matrix for Mongolian Tent Graph M r, 3 using Diagonal Matrix R.Malathi Assistant Professor of Mathematics SCSVMV, Enathur, Kanchipuram, Tamilnadu, India malathilathar@gmail.com Abstract: In graph theory, a Mongolian tent graph is defined as the graph obtained by adding an extra vertex above the graph and joining some of the other vertex of the top row to the additional vertex. Researchers have been using this concept effectively to different types of graphs. In this paper, we are going to discuss about the Mongolian tent graph’s Laplacian matrix (L= D-A where D is diagonal matrix of A and A is adjacent matrix) of M r, 3. Keywords: Vertex Labeling, Edge Labeling, Mongolian Tent Graph, Diagonal matrix, adjacent matrix, degree of vertex and edges. AMS Subject Classification: 05C78, 05C99

Medium Domination Number of a Mongolian Tent Graph R.Malathi Assistant Professor of Mathematics SCSVMV, Enathur, Kanchipuram, Tamilnadu, India malathilathar@gmail.com Abstract: In graph theory, some stability measures have been studied widely such as connectivity, edge-connectivity, integrity, tenacity, vertex covering and domination. These parameters take consideration into the neighborhood of edges and vertices. In a graph each vertex is capable of protecting every vertex in its neighborhood and in domination every vertex is required to be protected. In this paper, for any connected, undirected, loop less Mongolian tent graph we define the medium domination number of a Mongolian tent graph. The medium domination number is a notion which uses neighborhood of each pair of vertices. The main idea of this parameter is that each u, v ? V must be protected. So it is needed to examine how many vertices are capable of dominating both of u and v. Also the total number of vertices that dominate every pair of vertices and average value of this is defined as “the medium domination number” of a Mongolian tent graph. We establish general term of MD for Mongolian tent graph. AMS Subject Classification: 05C07, 05C69, 05C99 Key Words: Communication network, neighborhood, domination number, medium domination number.

Complete Undirected Graph in Coding R.Malathi S.Hemamalini Assistant Professor of Mathematics Author, CSE II year SCSVMV, Enathur, Kanchipuram, SCSVMV, Enathur, Kanchipuram, Tamilnadu, India Tamilnadu, India malathilathar@gmail.com hema13malini6@mail.com Abstract :The spectral graph theory studies the properties of graphs via the eigenvalues and eigenvectors of their associated graph matrices: the adjacency matrix and the graph Laplacian and its variants. Both matrices have been extremely well studied from an algebraic point of view. Using Turbo C++, we also have coded in C++ programming language and executed the Laplacian Matrix. The Laplacian allows a natural link between discrete representations, such as graphs, and continuous representations, such as vector spaces and manifolds. Given a complete undirected graph G with n vertices, its Laplacian of a diagonal matrix Lnxn is defined as L= D-A, Where A is the adjacency matrix of the graph and D is the diagonal matrix of A. Keywords: Complete graph, Laplacian matrix, adjacency matrix, diagonal matrix, coding and C++. AMS Classification : 05C50; 15A48

Complete Digraph in Coding R.Malathi S.Hemamalini Assistant Professor of Mathematics Author, CSE II year SCSVMV, Enathur, Kanchipuram, SCSVMV, Enathur, Kanchipuram, Tamilnadu, India Tamilnadu, India malathilathar@gmail.com hema13malini6@mail.com Abstract : Given a complete digraph G with n vertices, its Laplacian of a diagonal matrix Lnxn is defined as L= D-A, where A is the adjacency matrix of the graph and D is the diagonal matrix of A. Using Turbo C++ app we have also coded and executed the Laplacian matrix.The most important application of the Laplacian is spectral clustering that corresponds to a computationally tractable solution to the graph partitioning problem. Another application is spectral matching that solves for graph matching. Keywords: Complete digraph, Laplacian matrix, adjacency matrix, diagonal matrix, coding and C++. AMSClassification : 05C50; 15A18