International Journal of Mathematics and Soft Computing

13-19

Authors: Ujwala Nilkanth Deshmukh

In this paper we prove gracefulness and odd gracefulness of arbitrary super -subdivision of triangular snake, where labeling of the vertices follows arithmetic progression.

33-41

Authors: S K Vaidya, R M Pandit

The switching of a vertex $v$ of a graph $G$ means removing all the edges incident to $v$ and adding the edges joining $v$ to every vertex which is not adjacent to $v$ in $G$.The resultant graph is denoted by $\widetilde G$. In this paper, we explore the concept of independent domination in the context of switching of a vertex in a graph.

57-64

Authors: D Antony Xavier, Rosary Maria Singaraj, Elizabeth Thomas, Andrew Arokiaraj

Broadcasting is one of the types of global communication in interconnection networks. Broadcasting from a vertex of a graph is the simplest communication problem. In this paper, we analyse the broadcasting for bloom graph and prove that the broadcast time of bloom graph is at most two time units more than the optimal time.

75-85

Authors: Nithya Sai Narayana

The book graph denoted by $B_{n,2}$ is the cartesian product $S_{n+1} \times P_2$ where $S_{n+1}$ is a star graph with $n$ vertices of degree $1$ and one vertex of degree $n$ and $P_2$ is the path graph of $2$ vertices. Let $\tau(B_{n,2})$ denote the number of spanning trees of $B_{n,2}$. Let $X_{n,p}$ denote the generalized form of book graph where a family of $p$-cycles which are $n$ in number is merged at a common edge. In this paper, we discuss some recurrence relations satisfied by $X_{n,p}$ and spanning trees of these associated family of graphs.

97-104

Authors: D. K Thakkar, Ashish Amrutlal Prajapati

In this paper, we define minimal vertex covering sets with maximum cardinality in the given semigraph and the upper vertex covering number of a semigraph. We prove that this number does not increase when a vertex is removed from a semigraph. We also introduce well-covered semigraphs, approximately well covered semigraphs and proved some related results.

111-119

Authors: Vinayak K Gedam, Mahamad Banekhan Pathan

The main objective of transportation problem is to minimise the cost of shipping homogeneous commodity from various origins to various destinations. The classical transportation problem is extended by considering multiple incommensurate inputs and outputs for each shipment link. The relative efficiency concept is defined for each possible shipment link. Two linear programming models are proposed to determine the optimal transportation plan with maximum efficiency. A numerical example is discussed to show the applicability of said approach.

131-143

Authors: Santhi Maheswari, C Sekar

In this paper, edge irregular fuzzy graphs, edge totally irregular fuzzy graphs, highly edge irregular fuzzy graphs, highly edge totally irregular fuzzy graphs are introduced. Some properties of an edge irregular fuzzy graph and highly edge irregular fuzzy graphs are discussed in this paper. Edge irregularity and highly edge irregularity on some fuzzy graphs whose underlying crisp graphs are a cycle, a path, a star, a barbell graph are also studied.