International Journal of Mathematics and Soft Computing

1-11

Authors: Lekha Bijukumar, Avani Matad

A graph $G=(V(G),E(G))$ with $p$ vertices and $q$ edges is said to be an \textit{odd mean graph} if there is an injection $\textit{f}:V(G)\rightarrow\{0,1,2,\ldots,2q-1\}$ and the induced function $\textit{f*}:E(G)\rightarrow\{1,3,5,\ldots,2q-1\}$ defined as $f*(uv)=\begin{cases} \frac{f(u)+f(v)}{2}; \, \text{ if } f(u)+f(v) \text{ is even}\\ \frac{f(u)+f(v)+1}{2}; \, \text{ if } f(u)+f(v) \text{ is odd} \end{cases}$ is a bijection. In this paper we investigate some new families of odd mean graphs.

23-31

Authors: Gaurang V Ghodasara, Divya G Adalja

A graph $G=(V,E)$ is said to have a divisor cordial labeling if there is a bijection $f :V(G)\rightarrow\{1,2,\ldots|V(G)|\}$ such that if each edge $e=uv$ is assigned the label 1 if $f(u) | f(v) $ or $ f(v)| f(u)$ and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial graph. In this paper we derive divisor cordial labeling of ring sum of different graphs.

43-50

Authors: S K Vaidya, R M Pandit

A set $F \subseteq E(G) $ is an edge dominating set if each edge in $E(G)$ is either in $F$ or is adjacent to an edge in $F$. An edge dominating set $F$ is called a minimal edge dominating set if no proper subset $F ^ \prime$ of $F$ is an edge dominating set. The edge domination number $\gamma ^\prime(G)$ is the minimum cardinality among all minimal edge dominating sets. We investigate the edge domination number of some graphs called snakes which are obtained from path $P_n$ by replacing its edges by cycles $C_3$ and $C_4$.

57-63

Authors: K Monika, K Murugan

A $(p,q)$ graph $G=(V,E)$ is said to be an odd-even sum graph if there exists an injective function $f:V(G)\rightarrow\lbrace\pm 1,\pm 3 \pm 5, ...,\pm (2p-1)\rbrace$ such that the induced mapping $f^{*}:E(G)\rightarrow\lbrace 2,4,6, ...,2q\rbrace$ defined by $f^{*}(uv)=f(u)+f(v)~\forall~uv\in E(G)$ is bijective. The function $f$ is called an odd-even sum labeling of $G$. In this paper we study odd-even sum labeling of path $P_{n}(n\geq2)$, star $K_{1,n}(n\geq 1)$, bistar $B_{m,n}$,$S(K_{1,n})$, $B(m,n,k)$ and some standard graphs.

75-87

Authors: K Chitra Lakshmi, K Nagarajan

Let $G =(V,E)$ be a graph and $f$ be a mapping from $V(G) \rightarrow \left\{0,1,2 \right\}$. For each edge $uv$ assign the label \(\left\lceil\sqrt{f(u)f(v)}\right\rceil\), $f$ is called a geometric mean cordial labeling if $\mid v_f (i)- v_f (j)\mid \leq 1 $ and $\mid e_f (i)- e_f (j) \mid \leq1 $, where $v_f(x)$ and $e_f(x)$ denote the number of vertices and edges labeled with $x$, $x \in\left\{ 0,1,2 \right\}$ respectively. A graph with a geometric mean cordial labeling is called geometric mean cordial graph. In this paper geometric mean cordiality of some standard graphs such as path, star, cycle, complete graph, complete bipartite graph, wheel are discussed.

95-108

Authors: Ch Santhi Sundar Raj, S Nageswara Rao, M Santhi, K Ramanuja Rao

The notion of an Almost Distributive Lattice (abbreviated as ADL) is a common abstraction of several lattice theoretic generalization of Boolean algebras and Boolean rings. In this paper we introduce the notion of Relative pseudo-complementation on ADL's and discuss several properties of this.

117-125

Authors: U M Prajapati, B N Suthar

In this paper, we investigate prime labeling for some graphs obtained by duplication of graph elements and also we derive some result for $K_{2,n}$.Graph labeling, prime labeling, prime graph.