Iterated line digraphs arise naturally in designing fault tolerant systems. Diameter vulnerability measures the increase in diameter of a digraph when some of its vertices or arcs fail. Thus, the study of diameter vulnerability is a suitable approach to the fault tolerance of a network. In this article we present some upper bounds for diameter vulnerability of iterated line digraphs LkG. Our bo...

We derive several upper bounds on the spectral gap of Laplacian with standard or Dirichlet vertex conditions compact metric graphs. In particular, we obtain estimates based length a shortest cycle (girth), diameter, total graph, as well further quantities introduced here for first time, such avoidance diameter. Using known results about Ramanujan graphs, class expander also prove that some thes...

The result involution graph of a finite group , denoted by is an undirected simple whose vertex set the whole and two distinct vertices are adjacent if their product element. In this paper, graphs for all Mathieu groups connectivity in studied. diameter, radius girth also Furthermore, several other properties obtained.

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-zirodivisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

A total dominating set of a graph G with no isolated vertex is a set S of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

Let \({E}_{n}\) be the ring of Eisenstein integers modulo \(n\). We denote by \(G({E}_{n})\) and \(G_{{E}_{n}}\), unit graph unitary Cayley \({E}_{n}\), respectively. In this paper, we obtain value diameter, girth, clique number chromatic these graphs. also prove that for each \(n>1\), graphs \(G(E_{n})\) \(G_{E_{n}}\) are Hamiltonian.

During the 1997 Fédération Internationale des Sociétés d’Aviron World Junior Rowing Championships, anthropometric data on 383 male junior rowers were assessed. With 430 participating athletes, the sample represented 89% of the population. In addition to age, 27 dimensions were measured: body mass, six heights or lengths, four breadths, 10 girths, and six skinfolds. The elite male junior rowers ...

Given a simple connected graph G, let K(n) [2(n)] be the minimum cardinality of a set of vertices [edges], if any, whose deletion disconnects G and every remaining component has more than n vertices. For instance, the usual connectivity and the superconnectivity of G correspond to x(0) and ~c(1 ), respectively. This paper gives sufficient conditions, relating the diameter of G with its girth, t...