let g be a (p, q) graph. let k be an integer with 2 ≤ k ≤ p and f from v (g) to the set {1, 2, . . . , k} be a map. for each edge uv, assign the label |f(u) − f(v)|. the function f is called a k-difference cordial labeling of g if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

we give an algorithm, called t*, for finding the k shortest simplepaths connecting a certain pair of nodes, s and t, in a acyclic digraph.first the nodes of the graph are labeled according to the topologicalordering. then for node i an ordered list of simple s − i paths iscreated. the length of the list is at most k and it is created by usingtournament trees. we prove the correctness of t* and ...

Let $G$ be a $(p,q)$ graph. Let $f:V(G)to{1,2, ldots, k}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $left|t_{f}(i)-t_{f}(j)right|leq 1$, $i,j in {1,2, cdots,k}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labelled with $x$. A graph with a $k$-total prime cordi...

Let be a semigroup of words over an alphabet . Let consist of those elements of for which every prefix and suffix of belongs to . We show that is a free semigroup. Moreover, is called separative if also the complement is a semigroup. There are uncountably many separative semigroups over , if has at least two letters. We prove that if is separative, then every word has a unique minimum factoriza...

In this paper we study the structure of suffix trees. Given an unlabeled tree τ on n nodes and suffix links of its internal nodes, we ask the question “Is τ a suffix tree?”, i.e., is there a string S whose suffix tree has the same topological structure as τ? We place no restrictions on S, in particular we do not require that S ends with a unique symbol. This corresponds to considering the more ...

Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into reducing the space usage, leading ultimately to compressed suffix trees. These compressed data structures can efficiently simulate the suffix tree, while us...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....