Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating error model. In the Graph Edit Distance (GED) problem, insertion/deletion edges/nodes from one to another is explicitly expressed by At opposite, problem commonly referred as “graph matching” does not express such operations. For decades, thes...

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

Distance bounding (DB) emerged as a countermeasure to the so-called relay attack, which affects several technologies such as RFID, NFC, Bluetooth, and Ad-hoc networks. A prominent family of DB protocols are those based on graphs, which were introduced in 2010 to resist both mafia and distance frauds. The security analysis in terms of distance fraud is performed by considering an adversary that,...

We prove that every nite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.