Let G = (V, E) be a finite, simple and undirected graph having v = |V (G)| and e = |E(G)|. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) → {0, 1, 2, . . . , 2q−1} such that, when each edge xy is assigned the label |f(x)−f(y)|, the resulting edge labels are {1, 3, 5, . . . , 2q−1}. Motivated by the work of Z. Gao [6], we have defined odd graceful labeling f...

Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i. e. labellings of the nodes by distinct integers of the set {1, . . . , n} in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recurs...

Abstract argumentation frameworks (AFs) are one of the central formalisms in AI; equipped with a wide range of semantics, they have proven useful in several application domains. We contribute to the systematic analysis of semantics for AFs by connecting two recent lines of research – the work on input/output frameworks and the study of the expressiveness of semantics. We do so by considering th...

In this paper we establish that the Lovász θ function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM−θ graphs, on which Lovász θ function can be approximated well by a Support vector machine (SVM). We show that Erdös-Rényi random G(n, p) graphs are SVM−θ graphs for log4 n n ≤ p< 1. Even if we embed a large clique of size Θ (√ np 1−p ) in a G(n, p) graph ...

This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, and they can be regarded as partially ordered sets. We will study this connection between acyclic orientations of a graph and the theory of linear extensions or topological sor...

The term graceful degradation describes the smooth change to a lower state of some system aspect as a response to the occurrence of an event that prohibits the manifestation of the fully fledged system behavior. Graceful degradation has appeared in a variety of domains, from image processing and telecommunications to shared memory multiprocessors and multi-modular memory systems. In each domain...

In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C8 with some star graphs S1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C12 with some star graphs S1,r keeping two, three and five vertices gap betwee...