distance-balanced graphs are introduced as graphs in which every edge uv has the followingproperty: the number of vertices closer to u than to v is equal to the number of vertices closerto v than to u. basic properties of these graphs are obtained. in this paper, we study theconditions under which some graph operations produce a distance-balanced graph.

An edge irregular total k-labeling φ : V (G)∪E(G) → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights φ(x) + φ(xy) + φ(y) and φ(x′) + φ(x′y′) + φ(y′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. We have ...

Let G be a graph. A G-trade of volume m is a pair (T ,T ′), where each of T and T ′ consists of m graphs, pairwise edge-disjoint, isomorphic to G, such that T ∩T ′ = ∅ and the union of the edge sets of the graphs in T is identical to the union of the edge sets of the graphs in T ′. Let X(G) be the set of non-negative integers m such that no G-trade of volume m exists. In this paper we prove tha...

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...

The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs, as they compute a quadratic number of forces in each iteration. We give a new algorithm that takes only O(m + n log n) time per iteration when laying out a graph wi...

We give improved randomized (Monte Carlo) algorithms for undirected edge splitting and edge connectivity augmentation problems. Our algorithms run in time ~ O(n2) on n-vertex graphs, making them an ~ (m=n) factor faster than the best known deterministic ones on m-edge graphs.

A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

matroids are important combinatorial structures and connect close-lywith graphs. matroids and graphs were all generalized to fuzzysetting respectively. this paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. for a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. a fuzzy matroid, named graph fuzzy matro...

Edge-Path-Tree graphs are intersection graphs of Edge-Path-Tree matrices that is matrices whose columns are incidence vectors of edge-sets of paths in a given tree. Edge-Path-Tree graphs have polynomially many cliques as proved in [4] and [7]. Therefore, the problem of finding a clique of maximum weight in these graphs is solvable in strongly polynomial time. In this paper we extend this result...