International Journal of Mathematics and Soft Computing

1-9

Authors: Hariwan Zikri Ibrahim, A Mizyed

In this paper, we introduce and study the notion of semi-$\gamma$-$I$-open sets in ideal topological spaces and investigate some of their properties. Further, we study continuous functions on the above set and derive some of their properties.

29-38

Authors: Venkiteshwaran Sujitha

For a connected graph $G=(V,E)$, a set $S \subseteq E$ is called an \textit{edge-to-vertex geodetic set} of $G$ if every vertex of $G$ is either incident with an edge of $S$ or lies on a geodesic joining some pair of edges of $S$. The minimum cardinality of an edge-to-vertex geodetic set of $G$ is $g_{ev}(G)$. Any edge-to-vertex geodetic set of cardinality $g_{ev}(G)$ is called an \emph{edge-to-vertex geodetic basis} of $G$. A subset $T \subseteq S$ is called a \emph{forcing} subset for $S$ if $S$ is the unique minimum edge-to-vertex geodetic set containing $T$. A forcing subset for $S$ of minimum cardinality is a minimum forcing subset of $S$. The \emph{forcing edge-to-vertex geodetic number} of $S$, denoted by $f_{ev}(S)$, is the cardinality of a minimum forcing subset of $S$. The \emph{upper forcing edge-to-vertex geodetic number} of $G$, denoted by $f^{+}_{ev}(G)$, is $f^{+}_{ev}(G) = max \left\{f_{ev}(S)\right\}$, where the maximum is taken over all minimum edge-to-vertex geodetic sets $S$ in $G$. It is shown that the upper forcing edge-to-vertex geodetic number lies between 0 and $g_{ev}(G)$. Also, the upper forcing edge-to-vertex geodetic number of certain classes of graphs such as cycle, tree, complete graph and complete bipartite graph are determined.

49-56

Authors: V Kokilavani, M Vivek Prabu

In this paper, we define some new sets namely soft semi $^\#g\alpha$-border, soft semi $^\#g\alpha$-frontier and soft semi $^\#g\alpha$-exterior which are denoted by $\widetilde{s}$semi $^\#g\alpha$-bd(F,A), $\widetilde{s}$semi $^\#g\alpha$-fr(F,A) and $\widetilde{s}$semi $^\#g\alpha$-ext(F,A), where (F,A) is any soft set of (X,E) and also investigate their basic properties.

81-91

Authors: Medha Itagi Huilgol, Chitra Ramprakash

The concept of edge rotations and distance between graphs was introduced by Gary Chartrand et al. A graph $G$ can be transformed into a graph $H$ by an edge rotation if $G$ contains distinct vertices $u$,$v$ and $w$ such that $uv$ $\in $ $E(G)$, $uw$ $\notin$ $E(G)$ and $H$ $\cong$ $G - uv + uw$. In this paper we consider rotations on some snake related graphs followed by some general results.

107-120

Authors: Alias B Khalaf, Hariwan Zikri Ibrahim

In this paper, we introduce the notions of $\alpha_{\gamma}$-interior, $\alpha_{\gamma}$-neighbourhood, $\alpha_{\gamma}$-derived, $\alpha_{\gamma}$-boundary, $\alpha_{\gamma}$-kernel and $\alpha$-$\gamma$-g.closed set defined by $\gamma$-operation on $\alpha O(X)$ and investigate some of their properties.

133-142

Authors: S K Vaidya, N J Kothari

The concept of equi independent equitable domination is the combination of two important concepts, namely independent domination and equitable domination. A subset $D$ of $V(G)$ is called an equitable dominating set if for every $v \in V(G)-D$, there exists a vertex $u \in D$ such that $uv \in E(G)$ and $|deg(u)-deg(v)|\leq 1$. A vertex subset $D$ is said to be equitable independent set if any two vertices of $D$ are either non adjacent or if adjacent then their degrees differ by atleast 2. An equitable dominating set $D$ is said to be an equi independent equitable dominating set if it is also equitable independent set. The equi independent equitable domination number $i^e$ is the minimum cardinality of an equi independent equitable dominating set.

153-162

Authors: Haresh V Dedania, Milan Kantilal Kansagara

Let $G$ be an LCA group, $\om$ be a weight function on $G$, and $\A$ be a semisimple, commutative Banach algebra. We characterize some Banach algebra properties of vector-valued Beurling algebra $\Lgwa$ in terms of $\Lgw$ and $\A$ using the Bochner integration theory. These properties are unique uniform norm property (UUNP), unique $C^{\ast}$-norm property (UC$^{\ast}$NP), quasi divisor of zero property (QDZP), weak regularity (WR), regularity, and complete regularity (CR).

173-182

Authors: S S Sandhya, S Somasundaram, S Anusa

Let $G$ be a $(p,q)$ graph and $f:V(G)\leftarrow \{1,2,3,…,p+q \}$ be an injective function. For each edge $e=uv$ , let $f^*(e=uv)=\lceil \sqrt{\frac{f(u)^2+f(v)^2}{2}} \rceil$ or =\lfloor\sqrt{\frac{f(u)^2+f(v)^2}{2}} \rfloor$, then $f$ is called a super root square mean labeling if $f(V) \cup \{f^*(e):e \in E(G) \}=\{1,2,…,p+q \}. A graph that admits a super root square mean labeling is called as super root square mean graph. In this paper we prove that Double triangular snake, Alternate double triangular snake, Double quadrilateral snake and Alternate Double uadrilateral snake graphs are super root square mean graphs. Keywords: Root Square mean graph, Super Root Square mean graph, Triangular snake, Double triangular snake, Quadrilateral snake, Double quadrilateral snake.