منابع مشابه
On Eulerian irregularity in graphs
A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G i...
متن کاملThe irregularity and total irregularity of Eulerian graphs
For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.
متن کاملOn Making Directed Graphs Eulerian
A directed graph is called Eulerian, if it contains a tour that traverses every arc in the graph exactly once. We study the problem of Eulerian Extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold. This problem is motivated through applications in vehicle rou...
متن کامل240 on Graphs of Irregularity Strength 2
We consider undirected graphs without loops or multiple edges. A weighting of a graph G is an assignment of a positive integer w( e) to each edge of G. For a vertex x€V(G), the (weighted) degree d(x) is the sum ofweights on the edges ofG incident to x. The irregularity strength s( G) of a graph G was introduced by Chartrand et al. in [1] a.s the minimum integer t such that G has a weighting wit...
متن کاملOn total vertex irregularity strength of graphs
Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2014
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1744