Related papers: Edge Quasi $\lambda$-distance-balanced Graphs in M…
In a graph A, for each two arbitrary vertices g, h with d(g,h)=2,|MAg2h|=mAg2h is introduced the number of edges of A that are closer to g than to h. We say A is a 2-edge distance-balanced graph if we have mAg2h=mAh2g. In this article, we…
For every pair of vertices u and v with d(u; v) = n, Wun G v denotes the set of all vertices of G that are closer to u than to v. In this paper, we introduce quasi-({\lambda}; n)-distance-balanced graphs and then study some properties of…
A connected and nonempty graph A is defined as generalized t-edge distance-balanced, while for each edge f={\alpha}\{beta} the number of edges nearer to {\alpha} than \{beta} are equal to t-times of edges nearer to \{beta} than to {\alpha},…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}.…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that…
Let $G(V, E)$ be a simple connected graph, with $|E| = \epsilon.$ In this paper, we define an edge-set graph $\mathcal G_G$ constructed from the graph $G$ such that any vertex $v_{s,i}$ of $\mathcal G_G$ corresponds to the $i$-th…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
A graph $X$ is said to be {\it distance--balanced} if for any edge $uv$ of $X$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. A graph $X$ is said to be {\it strongly…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a…
This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative…
Given a connected graph $G(V, E)$, the edge dimension, denoted $\mathrm{edim}(G)$, is the least size of a set $S \subseteq V$ that distinguishes every pair of edges of $G$, in the sense that the edges have pairwise distinct tuples of…
Let $\ell$ denote a positive integer. A connected graph $\G$ of diameter at least $\ell$ is said to be $\ell${\it -distance-balanced} whenever for any pair of vertices $u,v$ of $\G$ such that $d(u,v)=\ell$, the number of vertices closer to…
Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…
A nonempty graph G is called generalized 3-distance-balanced, (3-GDB) whenever for every edge ab, |Wab|=3|Wba| or conversely. As well as a graph G is called generalized 3-nicely distance-balanced (3-GNDB) whenever for every edge ab of G,…
A graph $\Gamma$ is said to be distance-balanced if for any edge $uv$ of $\Gamma$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$, and it is called nicely distance-balanced if…
Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…