Throughout this paper, we present a new class of graphs so-called n-edgedistance-balanced graphs inspired by the concept of edge-distance-balanced property initially introduced by Tavakoli et al. [Tavakoli M., Yousefi-Azari H., Ashrafi A.R., Note on edge distance-balanced graphs, Trans. Combin. 1 (1) (2012), 1-6]. Moreover, we propose some characteristic results to recognize 2-edge-distance-bal...

In this paper, we discuss balanced bipolar intuitionistic fuzzy graphs and study some of their properties 1.Introduction Graph theory is developed when Euler gave the solution to the famous Konigsberg bridge problem in 1736. Graph theory is very useful as a branch of combinatorics in the field of geometry, algebra, number theory, topology, operations research, optimization and computer science....

For a graph G and not necessarily proper k-edge coloring c:E(G)→{1,…,k}, let mi(G) be the number of edges color i, call color-balanced if mi(G)=mj(G) for every two colors i j. Several famous open problems relate to this notion; Ryser's conjecture on transversals in latin squares, instance, is equivalent statement that properly n-edge colored complete bipartite Kn,n has perfect matching. We cont...

A {0, 1}-matrix A is balanced if it does not contain a submatrix of odd order having exactly two 1’s per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrarily to what happened for perfect graphs. In this paper, we provide such a chara...