Dujmović et al. [J. ACM '20] proved that every planar graph is isomorphic to a subgraph of the strong product bounded treewidth and path. Analogous results were obtained for graphs Euler genus or apex-minor-free graphs. These tools have been used solve longstanding problems on queue layouts, non-repetitive colouring, p-centered adjacency labelling. This paper proves analogous structure theorems...

I.Cahit introduced cordial graphs as a weaker version of graceful and harmonious graphs. The total product cordial labeling is a variant of cordial labeling. In this paper we introduce a vertex analogue product cordial labeling as a variant of total product cordial labeling and name it as total vertex product cordial labeling. Finally, we investigate total vertex product cordial labeling for ma...

Classical warranty plans require crisp data obtained from strictly controlled reliability tests. However, in a real situation these requirements might not be fulfilled. In an extreme case, the warranty claims data come from users whose reports are expressed in a vague way. Furthermore, there are special situations where several characteristics are used together as criteria for judging the warra...

The notion of uncertainty in expert systems is dealing with vague data, incomplete information, and imprecise knowledge. Different uncertainty types which are imprecision, vagueness, ambiguity, and inconsistence need different handling models. Uncertain knowledge representation and analysis is an essential issue. Classical probability, Bayes theory, Dempster–Shafer theory, certainty factor and ...