Abstract The cubic fuzzy graph structure, as a combination of graphs and structures, shows better capabilities in solving complex problems, especially cases where there are multiple relationships. quality method determining the degree vertices this type simultaneously supports membership interval-valued membership, addition to multiplicity relations, motivated us conduct study on maximal produc...

Let A ⊆ V(H) of any graph H, every node w H be labeled using a set numbers; , where d(w,v) denotes the distance between and v in known as its open A-distance pattern. is distance-pattern uniform (odpu)-graph, if there nonempty subset ⊆V(H) together with same for all . Here pattern (odpu-) labeling an odpu-set H. The minimum cardinality vertices it exists, will odpu-number This article gives cha...

Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far exact (exponential) treewidth algorithm. Based on the recent results of Mazoit, we define the structures that can be regarded as minimal tri...

We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in the Bron–Kerbosch algorithm. All the maximal cliques generated are output in a tree-like form. Subsequently, we prove that its worst-case time complexity is O(3n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3n/3...

By prior work, there is a distributed graph algorithm that finds a maximal fractional matching (maximal edge packing) in O(∆) rounds, independently of n; here ∆ is the maximum degree of the graph and n is the number of nodes in the graph. We show that this is optimal: there is no distributed algorithm that finds a maximal fractional matching in o(∆) rounds, independently of n. Our work gives th...

Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are ...

In this paper, we find lower bounds for the maximum and minimum numbers of cliques in maximal sets of pairwise disjoint cliques in a graph . By complementation, these yield lower bounds for the maximum and minimum numbers of independent sets in maximal sets of pairwise disjoint maximal independent sets of vertices in a graph . In the latter context, we show by examples that one of our bounds is...

A greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empty. We have recently shown that any greedy clique decomposition of a graph of order n has at most-~ cliques. A greedy max-clique decomposition is a particular kind of greedy clique decomposition where maximum cliques are removed, instead of just maximal ones. In this pa...