Kramer-Mesner matrices have been used as a powerful tool to construct t-designs. In this paper we construct Kramer-Mesner matrices for xed values of k and t in which the entries are polynomials in n the number of vertices of the underlying graph. From this we obtain an elementary proof that with a few exceptions S 2] n is a maximal subgroup of S (n 2) or A (n 2). We also show that there are onl...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

Let G be an infinite connected graph. We introduce two kinds of multilinear fractional maximal operators on G. By assuming that the graph satisfies certain geometric conditions, we establish bounds for above endpoint Sobolev spaces and Hajłasz–Sobolev

This paper compares several published algorithms which list all of the maximal cliques of a graph. A clique is a complete subgraph, i.e., a set of vertices and edges such that every pair of vertices is joined by an edge. A maximal clique is a clique which is not a proper subgraph of a larger clique. A closely related concept is that of a maximal independent set (MIS), where every pair of vertic...

A graph G = (V, E) is called a split graph if there exists a partition V = I ∪K such that the subgraphs G[I ] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a split graph G with |I | < |K| to be hamiltonian. We will call a split graph G with |I | < |K| satisfying this condition a Burkard-Hammer graph. Furt...

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 obtai...

Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that for each p ∈ P either b ≤P p for some b ∈ B or p ≤p c for some c ∈ C. We construct both splitting and non-splitting infinite maximal antichains in G and in D. A point y ∈ P is a cut point in a pose...

As a consequence of an early result of Pach we show that every maximal triangle-free graph is either homomorphic with a member of a speciic innnite sequence of 3-colourable graphs or it contains the Petersen graph minus one vertex as a subgraph. From this result and further structural observations we derive that if a (not necessarily maximal) triangle-free graph of order n has minimum degree n=...

We determine the maximal cocliques of size ≥ 4q2 + 5q + 5 in the Kneser graph on point-plane flags in PG(4, q). The maximal size of a coclique in this graph is (q2 + q + 1)(q3 + q2 + q + 1).

NP-complicated problems have been described in the graph theory. An example is the extracting of all maximal cliques from a graph. Many algorithms for solving this problem have been described. However, complexity is linear to the number of maximal cliques. This paper discusses a new approach for extracting maximal cliques, based on the monotone system theory. The complexity of the presented alg...