Journal of Algorithms and Computation
Volume:49 Issue: 2, Dec 2017

Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a binary tree can be determined. We present the algorithm BT-LEAF, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.

Let G be a graph with p vertices and q edges. The graph G is said to be a super pair sum labeling if there exists a bijection f from V(G)cup E(G) to {0, pm 1, pm2, dots, pm (frac{p+q-1}{2})} when p+q is odd and from V(G)cup E(G) to {pm 1, pm 2, dots, pm (frac{p+q}{2})} when p+q is even such that f(uv)=f(u)+f(v). A graph that admits a super pair sum labeling is called a {it super pair sum graph}. Here we study about the super pair sum labeling of some standard graphs.the formula is not displayed corretly!

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studiedcite{mss}. Computing chromatic sum of an arbitrary graph introduced by Kubica [1989] is known as NP-complete problem. Graph coloring is the most studied problem of combinatorial optimization. As an advancement fuzzy coloring of a fuzzy graph was defined by authors Eslahchi and Onagh in 2004, and later developed by them as Fuzzy vertex coloringcite{eo} in 2006.This fuzzy vertex coloring was extended to fuzzy total coloring in terms of family of fuzzy sets by Lavanya. S and Sattanathan. Rcite{sls}. In this paper we are introducing textquotedblleft Just Chromatic excellence in fuzzy graphstextquotedblright.

In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity. Since we are primarily interested in the case where disruption of the graph is caused by the removal of a vertex or vertices (and the resulting loss of all edges incident with the removed vertices), we shall restrict our discussion to vertex stability measures. In the interest of completeness, however, we have included several related measures of edge stability.

In this paper we generalize the remainder cordial labeling, called $k$-remainder cordial labeling and investigate the $4$-remainder cordial labeling behavior of certain graphs.

One widespread procedure to render the attractor of Kleinian groups, appearing in the renown book [8], wantshuge memory resources to compute and store the results. We present a new faster and lighter version that drops the original array and pulls out group elements from integers.

Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called  $lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Sugeno-Weber t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Sugeno-Weber composition and present some necessary and sufficient conditions for determining the feasibility of the problem. Also, two procedures are presented for simplifying the problem. Since the feasible solutions set of FREs

In this paper, a new  algorithm for computing secondary invariants of  invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants.  The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to implement.

Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kronecker products and matrix manipulations. Specifically, the eigensolution of the corresponding regular mechanical system was inserted in the algorithm to further accelerate the solution. The developed method allowed reduction in computational complexity (i.e., $mathrm{O}(n^2)$) when compared to earlier methods. The application of the method was indicated using a simple example.

In this paper we introduce the concept of $(1,2)^*$-sb-separated sets and $(1,2)^*$-soft b-connected spaces and prove some properties related to these break topics. Also we disscused the properties of $(1,2)^*$-soft b- compactness in soft bitopological space.the formula is not displayed correctly!

Let G be a (p,q) graph and A be a group. We denote the order of an element a in A by o(a).  Let f:V(G)rightarrow A be a function. For each edge uv assign the label 1 if (o(f(u)),o(f(v)))=1 or 0 otherwise. f is called a group A Cordial labeling if |v_f(a)-v_f(b)| leq 1 and |e_f(0)- e_f(1)|leq 1, where v_f(x) and e_f(n) respectively denote the number of vertices labelled with an element x and number of edges labelled with n (n=0,1). A graph which admits a group A Cordial labeling is called a group A Cordial graph. In this paper we define group {1 ,-1 ,i ,-i} Cordial graphs and characterize the graphs C_n + K_m (2 leq m leq 5) that  are group {1 ,-1 ,i ,-i} Cordial.the formula is not displayed correctly!

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters.  Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.