1,720,958 research outputs found
Distance measures in graphs
No full textThis thesis details the results of an investigation of bounds on four distances measures,
namely, radius, diameter, the Gutman index and the edge-Wiener index, in
terms of other graph parameters, namely, order, irregularity index and the three
classical connectivity measures, minimum degree, vertex-connectivity and edgeconnectivity.
The thesis has six chapters. In Chapter 1, we de ne the most important terms used
throughout the thesis and we also give a motivation for our research and provide
background for relevant results. In this chapter we include the importance of the
distance measures to be studied.Chapter 2 focuses on the radius, diameter and the degree sequence of a graph. We
give asymptotically sharp upper bounds on the radius and diameter of
(i) a connected graph,
(ii) a connected triangle-free graph,
(iii) a connected C4-free graph of given order, minimum degree, and given number
of distinct terms in the degree sequence of the graph.
We also give better bounds for graphs with a given order, minimum degree and
maximum degree. Our results improve on old classical theorems by Erd os, Pach,
Pollack and Tuza [24] on radius, diameter and minimum degree.In Chapter 3, we deal with the Gutman index and minimum degree. We show that for nite connected graphs of order n and minimum degree , where is a
constant, Gut(G) 24 3
55( +1)n5 +O(n4). Our bound is asymptotically sharp for every
2 and it extends results of Dankelmann, Gutman, Mukwembi and Swart [18]
and Mukwembi [43], whose bound is sharp only for graphs of minimum degree 2:
In Chapter 4, we develop the concept of the Gutman index and edge-Wiener index in
graphs given order and vertex-connectivity. We show that Gut(G) 24
55 n5 +O(n4)
for graphs of order n and vertex-connectivity , where is a constant. Our bound
is asymptotically sharp for every 1 and it substantially generalizes the bound
of Mukwembi [43]. As a corollary, we obtain a similar result for the edge-Wiener
index of graphs of given order and vertex-connectivity.Chapter 5 completes our study of the Gutman index, the edge-Wiener index and
edge-connectivity. We study the Gutman index Gut(G) and the Edge-Wiener index
We(G) of graphs G of given order n and edge-connectivity . We show that the
bound Gut(G) 24 3
55( +1)n5 + O(n4) is asymptotically sharp for 8. We improve
this result considerably for 7 by presenting asymptotically sharp upper bounds
on Gut(G) and We(G) for 2 7.
We complete our study in Chapter 6 in which we use techniques introduced in
Chapter 5 to solve new problems on size. We give asymptotically sharp upper
bounds on the size, m of (i) a connected triangle-free graph in terms of order, diameter and minimum
degree,(ii) a connected graph in terms of order, diameter and edge-connectivity,
(iii) a connected triangle-free graph in terms of edge-connectivity, order and diameter.
The result is a strengthening of an old classical theorem of Ore [49] if edge-connectivity
is prescribed and constant
Distance Measures in Graphs
No full textThis thesis details the results of an investigation of bounds on four distances measures,
namely, radius, diameter, the Gutman index and the edge-Wiener index, in
terms of other graph parameters, namely, order, irregularity index and the three
classical connectivity measures, minimum degree, vertex-connectivity and edgeconnectivity.
The thesis has six chapters. In Chapter 1, we define the most important terms used
throughout the thesis and we also give a motivation for our research and provide
background for relevant results. In this chapter we include the importance of the
distance measures to be studied.
Chapter 2 focuses on the radius, diameter and the degree sequence of a graph. We
give asymptotically sharp upper bounds on the radius and diameter of
(i) a connected graph,
(ii) a connected triangle-free graph,
(iii) a connected C4-free graph of given order, minimum degree, and given number
of distinct terms in the degree sequence of the graph.
We also give better bounds for graphs with a given order, minimum degree and
maximum degree. Our results improve on old classical theorems by Erdös, Pach,
Pollack and Tuza [24] on radius, diameter and minimum degree.
In Chapter 3, we deal with the Gutman index and minimum degree. We show that for finite connected graphs of order n and minimum degree δ, where δ is a
constant, Gut(G) 24_355(n+1)n5 +O(n4). Our bound is asymptotically sharp for every
= 2 and it extends results of Dankelmann, Gutman, Mukwembi and Swart [18]
and Mukwembi [43], whose bound is sharp only for graphs of minimum degree 2:
In Chapter 4, we develop the concept of the Gutman index and edge-Wiener index in
graphs given order and vertex-connectivity. We show that Gut(G) =24
55_n5 +O(n4)
for graphs of order n and vertex-connectivity δ, where δ is a constant. Our bound
is asymptotically sharp for every δn 1 and it substantially generalizes the bound
of Mukwembi [43]. As a corollary, we obtain a similar result for the edge-Wiener
index of graphs of given order and vertex-connectivity.
Chapter 5 completes our study of the Gutman index, the edge-Wiener index and
edge-connectivity. We study the Gutman index Gut(G) and the Edge-Wiener index
We(G) of graphs G of given order n and edge-connectivity _. We show that the
bound Gut(G) 24_3
55(n+1)n5 + O(n4) is asymptotically sharp for 8. We improve
this result considerably for 7 by presenting asymptotically sharp upper bounds
on Gut(G) and We(G) for 2 7.
We complete our study in Chapter 6 in which we use techniques introduced in
Chapter 5 to solve new problems on size. We give asymptotically sharp upper
bounds on the size, m of
(i) a connected triangle-free graph in terms of order, diameter and minimum
degree,
(ii) a connected graph in terms of order, diameter and edge-connectivity,
(iii) a connected triangle-free graph in terms of edge-connectivity, order and diameter.
The result is a strengthening of an old classical theorem of Ore [49] if edge-connectivity
is prescribed and constant
The Gutman Index and the Edge-Wiener Index of Graphs with Given Vertex-Connectivity
No full textThe Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of re- search on graph indices is to bound indices in terms of the order and other parameters of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area
The Gutman Index and the Edge-Wiener Index of Graphs with given Vertex-Connectivity
No full textThe Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of re- search on graph indices is to bound indices in terms of the order and other parameters of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area.The work of T. Vetr´ık has been supported by the National Research Foundation of South Africa; Grant numbers: 91499, 90793
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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