Wide diameter dω(G) and fault-diameter Dω(G) of an interconnection network G have been recently studied by many authors. We determine the wide diameter and fault-diameter of the integer simplex T n m. Note that d1(T n m) = D1(T n m) = d(T n m), where d(T n m) is the diameter of T n m. We prove that dω(T n m) = Dω(T n m) = d(T n m) + 1 when 2 ≤ ω ≤ n. Since a triangular pyramid TPL is T 3 L, we ...

The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)+d(v)} $ of all edges $ uv $ of $G$, where $d(u)$ denotes the degree of the vertex $u$ in $G$. In this work, we prove the conjecture $dfrac{H(G)}{D(G)} geq dfrac{1}{2}+dfrac{1}{3(n-1)}  $ given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound $ dfrac{H(G)}{D(G)}geq dfra...

OBJECTIVE The objective of the present study was to assess the effect of tobacco chewing on buccal mucosa by using cytomorphometry. STUDY DESIGN We compared the cellular diameter (CD), nuclear diameter (ND) and the ratio of nuclear diameter to cellular diameter (N/C) of buccal mucosa squames of normal subjects (N) with buccal mucosa squames of tobacco users without lesion (A), with tobacco-li...

In this study the effects of plant growth regulators including; GA3 (0 and 50 mg/l) and ethephon (0 and 500 mg/l) were studied on the quality properties of two grape cultivars (Perlette and Yaghuti). At the harvest time, some physicochemical characteristics such as fruit cluster weight, fruit diameter, length, volume and L/D ratio, flesh firmness, fresh weight, TA, pH, TSS and fruit color were ...

We define a graph G = (V, E) with m = \E\ edges, n = \V\ vertices, maximum degree D, and diameter d, to be d-critical if it has the property that for any edge e G E, the graph G — e has diameter > d. We explore some results relating to a conjecture on the maximum possible number of edges in a 2-critical graph. We also present efficient algorithms for identifying spanning d-critical subgraphs of...

A graph is called vertex diameter critical if its diameter increases when any vertex is removed. Regular vertex diameter critical graphs of every valency k ≥ 2 and diameter d ≥ 2 exist, raising the question of identifying the smallest such graphs. We describe an infinite family of k-regular vertex diameter critical graphs of diameter d with at most kd+ (2k − 3) vertices. This improves the previ...

any defects in street trees may cause injuries to human, vehicles and buildings. this research was investigated in the babol city, mazandaran province, in the northern state of iran.used the perfect inventory methods and measured the diameter at breathe height (dbh), height and hazardous criteria (dead woods, cracks or seams, decay, wound or cankers, root problems, weak branch unions and skew f...

We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d ≤ 1000 via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most d in O(d5) time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integra...

Concern about fault tolerance in the design of interconnection networks has aroused interest in finding large graphs such that the subgraphs obtained by deleting any set of up to s vertices have small diameter. Clearly, 1 ≤ s ≤ ∆ − 1, where ∆ is the maximum degree of the graph. Graphs of maximum degree ∆, diameter ≤ D and such that the graphs obtained by deletion of up to s vertices have diamet...

We construct a family of Cayley digraphs of degree d, diameter k and order kbd/2ck for any d ≥ 4 and k ≥ 3. We also present a collection of bipartite Cayley digraphs of order at least (k − 1)bd/2ck−1 for any degree d ≥ 4 and diameter k ≥ 4. For sufficiently large d and k, our digraphs are the largest known Cayley digraphs of degree d and diameter k, where k 6= d − 1 or d, and our bipartite digr...