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Spanning tree results for graphs and...

Gross, Daniel J.

Spanning tree results for graphs and multigraphs :a matrix-theoretic approach /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spanning tree results for graphs and multigraphs :Daniel J. Gross, John T. Saccoman, Charles L. Suffel.
其他題名:	a matrix-theoretic approach /
作者:	Gross, Daniel J.
其他作者:	Saccoman, John T.,
出版者:	Hackensack, NJ :World Scientific,c2015.
面頁冊數:	x, 175 p. :ill. ;24 cm.
標題:	Graph theoryData processing.
ISBN:	9789814566032 (hbk.) :

Spanning tree results for graphs and multigraphs :a matrix-theoretic approach /
Gross, Daniel J.

Spanning tree results for graphs and multigraphs :a matrix-theoretic approach /Daniel J. Gross, John T. Saccoman, Charles L. Suffel. - Hackensack, NJ :World Scientific,c2015. - x, 175 p. :ill. ;24 cm.

Includes bibliographical references (p. 169-171) and index.

0. An introduction to relevant graph theory and matrix theory. 0.1. Graph theory. 0.2. Matrix theory -- 1. Calculating the number of spanning trees: The algebraic approach. The node-arc incidence matrix. 1.2. Laplacian matrix. 1.3. Special graphs. 1.4. Temperley's B-matrix. 1.5. Multigraphs. 1.6. Eigenvalue bounds for multigraphs. 1.7. Multigraph complements. 1.8. Two maximum tree results -- 2. Multigraphs with the maximum number of spanning Trees: An analytic approach. 2.1. The maximum spanning tree problem. 2.2. Two maximum spanning tree results -- 3. Threshold graphs. 3.1. Characteristic polynomials of threshold graphs. 3.2. Minimum number of spanning trees -- 4. Approaches to the multigraph problem -- 5. Laplacian integral graphs and multigraphs. 5.1. Complete graphs and related structures. 5.2. Split graphs and related structures. 5.3. Laplacian integral multigraphs.

This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theoretic approach to the calculation of the number of spanning trees. The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all stripes, including mathematicians, computer scientists, electrical and computer engineers, and operations researchers.--

ISBN: 9789814566032 (hbk.) :NT$2038

LCCN: 2014497378Subjects--Topical Terms:

296758
Graph theory
--Data processing.

LC Class. No.: QA166 / .G756 2015

Spanning tree results for graphs and multigraphs :a matrix-theoretic approach /
LDR:02407nam a2200229 a 4500 001 457904
003 DLC
005 20150225114058.0
008 150922s2015 njua b 001 0 eng d
010 $a 2014497378
020 $a 9789814566032 (hbk.) : $c NT$2038
020 $a 9814566039 (hbk.)
035 $a (OCoLC)ocn861207554
035 $a 2014497378
040 $a BTCTA $b eng $c BTCTA $d YDXCP $d CDX $d CUS $d DLC
042 $a lccopycat
050 0 0 $a QA166 $b .G756 2015
100 1 $a Gross, Daniel J. $q (Daniel Joseph) $3 709071
245 1 0 $a Spanning tree results for graphs and multigraphs : $b a matrix-theoretic approach / $c Daniel J. Gross, John T. Saccoman, Charles L. Suffel.
260 $a Hackensack, NJ : $b World Scientific, $c c2015.
300 $a x, 175 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references (p. 169-171) and index.
505 0 $a 0. An introduction to relevant graph theory and matrix theory. 0.1. Graph theory. 0.2. Matrix theory -- 1. Calculating the number of spanning trees: The algebraic approach. The node-arc incidence matrix. 1.2. Laplacian matrix. 1.3. Special graphs. 1.4. Temperley's B-matrix. 1.5. Multigraphs. 1.6. Eigenvalue bounds for multigraphs. 1.7. Multigraph complements. 1.8. Two maximum tree results -- 2. Multigraphs with the maximum number of spanning Trees: An analytic approach. 2.1. The maximum spanning tree problem. 2.2. Two maximum spanning tree results -- 3. Threshold graphs. 3.1. Characteristic polynomials of threshold graphs. 3.2. Minimum number of spanning trees -- 4. Approaches to the multigraph problem -- 5. Laplacian integral graphs and multigraphs. 5.1. Complete graphs and related structures. 5.2. Split graphs and related structures. 5.3. Laplacian integral multigraphs.
520 $a This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theoretic approach to the calculation of the number of spanning trees. The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all stripes, including mathematicians, computer scientists, electrical and computer engineers, and operations researchers.-- $c Source other than Library of Congress.
650 0 $a Graph theory $x Data processing. $3 296758
650 0 $a Graph theory $x Research. $3 709074
700 1 $a Saccoman, John T., $d 1964. $3 709072
700 1 $a Suffel, Charles. $3 709073