منابع مشابه
The 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 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 کاملOn Total Edge Irregularity Strength of Staircase Graphs and Related Graphs
Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics
سال: 2019
ISSN: 2217-5539,2466-3778
DOI: 10.5937/spsunp1902097m