The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the k-subspaces of Fq, and are adjacent if they intersect in a (k− 1)-subspace) for k ≥ 2. We find an upper bound on its metric dimension, which is ...

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

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The objective of this paper is to describe the concept intuitionistic fuzzy metric-like spaces. This space an extension spaces and metric spaces, We discuss convergence sequences, contractive mapping some fixed-point theorems in space. also give explanations, examples counterexamples validate superiority these results. Our results provide a substantial several important from

Abstract In this article we make an improvement in the Banach contraction using a controlled function metric like spaces, which generalizes many results literature. Moreover, present application on Fredholm type integral equation.