Let mcm(m,n) and mwm(m,n,N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let mcmbi,mwmbi be their counterparts for bipartite graphs, where m,n, and N are the edge count, vertex count, and maximum integer edge weight. Kao, Lam, Sung, and Ting [1] gave a general reduction showing mwmbi(m,n,N) = O(N ·mcmbi(m,n)) and Huang and Kavitha [2] recent...

We provide a lower bound for the spectral radius of the universal cover of irregular graphs in the presence of symmetric edge weights. We use this bound to derive an Alon-Boppana type bound for the second eigenvalue of the normalized Laplacian.

1 Edge-disjoint decompositions Some of the graphs in this section are allowed to have multiple edges. They will be referred to as multigraphs. All graphs are assumed to have vertex set [n] = {1, 2, . . . , n}. Multiple edges between vertices of a multigraph G are regarded as distinct members of its edge set, E(G). We say that a collection of multigraphs1 Gi, i ∈ [m] is an edge-disjoint decompos...

Abstract In this paper, first we introduce the concepts of interval valued m -polar fuzzy (briefly, IV PF) p -ideals, PF q -ideals and a in BCI-algebras. Then show that ( )-ideals are ideals but converse statements not valid an example is given each case. We provide conditions under which ideal becomes )-ideal. Further, associated properties considered. Moreover, characterize terms Also, corres...

edge distance-balanced graphs are graphs in which for every edge $e = uv$ the number of edges closer to vertex $u$ than to vertex $v$ is equal to the number of edges closer to $v$ than to $u$. in this paper, we study this property under some graph operations.

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 ...

In this paper we discuss the edge-bandwidth of some families of graphs and characterize graphs by edge-bandwidth. In particular, bounds for m × n grids, triangular grids of size l, and the closure of the triangular grid T * l .

Given a graph G and an integer k ≥ 0, the NP-complete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]-har...

We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative coefficients. A combinatorial explanation of this phenomenon involves loop-erased walks. Applications include total positivity of hitting matr...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.