In this paper we prove, that the problem ”kdim(G) ≤ 3” is polynomially solvable for chordal graphs, thus partially solving the problem of P. Hlineny and J. Kratochvil. We show, that the problem of finding m-krausz dimension is NP-hard for every m ≥ 1, even if restricted to (1,2)-colorable graphs, but the problem ”kdimm(G) ≤ k” is polynomially solvable for (∞, 1)-polar graphs for every fixed k,m...

Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L-fuzzy setting are presented. Independent M-fuzzifying set system is introduced and some of its properties are discussed. Further independent (L,M)-fuzzy set system is given and some of its properties are obtained. The relations of th...

let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...

The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a pmedian with respect to the new edge lengths. The problem is shown to be strongly NP-hard on general graphs and weakly NP-hard on series-parallel graphs. Therefore, the special case on...

Matrix M is k-concise if the finite entries of each column of M consist of k or fewer intervals of identical numbers. We give an O(n + m)-time algorithm to compute the row minima of any O(1)-concise n×m matrix. Our algorithm yields the first O(n+m)-time reductions from the replacement-paths problem on an n-node m-edge undirected graph (respectively, directed acyclic graph) to the single-source ...

Let D be the minimum dominating set of intuitionistic fuzzy graph G. The minimum intuitionistic fuzzy cardinality of all edge dominating set of intuitionistic fuzzy graph G is known as edge domination number and it is denoted by γe(G). In this Paper, we initiate some definitions onedge dominating set concerning intuitionistic fuzzy sets. Further, we investigate some results onedge domination nu...

Interval graphs—the intersection graphs of one dimensional intervals—are considered one of the most useful mathematical structures to model real life applications [18]. Interval graphs have been widely studied since they first appeared in the literature in 1957. In 1976, Booth and Lueker [7] introduced a data structure called PQ-trees that could recognize interval graphs in linear time; since t...

Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

The 1–2–3 Conjecture, raised by Karoński, Łuczak and Thomason, states that almost every graph G admits a proper 3-labelling, i.e., labelling of the edges with 1, 2, 3 such no two adjacent vertices are incident to same sum labels. Another interpretation this conjecture, may be attributed Chartrand et al., is can turned into locally irregular multigraph M, having degree, replacing each its at mos...

We describe the use of two-graphs and skew (oriented) two-graphs as isomorphism invariants for translation planes and m-systems (including ovoids and spreads) of polar spaces in odd characteristic.