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Abstrak :
This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homomorphisms and colorings and the uniqueness of the Mycielskian up to isomorphism. This book also introduces several interesting topics such as Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices, and a concrete application of triangulated graphs.

Abstrak :
This well-organized reference is a definitive encyclopedia for the literature on graph classes. It contains a survey of more than 200 classes of graphs, organized by types of properties used to define and characterize the classes, citing key theorems and literature references for each. The authors state results without proof, providing readers with easy access to far more key theorems than are commonly found in other mathematical texts. Interconnections between graph classes are also provided to make the book useful to a variety of readers.

Abstrak :
This book constitutes the proceedings of the 6th International Conference on Graph Transformations, ICGT 2012, held in Bremen, Germany, in September 2012. The 30 papers and 3 invited papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on behavioural analysis, high-level graph transformation, revisited approaches, general transformation models, structuring and verification, graph transformations in use, (meta-)model evolution and incremental approaches.

Abstrak :
Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics. The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises.

Abstrak :
Penelitian pendahuluan ini mempunyai tujuan untuk menghasilkan formalisasi sebagian dari teori graph. Graph merupakan ilmu yang cakupannya luas dan mempunyai banyak aplikasi. Akan tetapi, di dalam pustaka sistem HOL belum terdapat teori graph yang formal. Penyusunan formalisasi diawali dengan studi literatur mengenai sistem HOL, kemudian dilanjutkan dengan eksperimen-eksperimen. Terdapat enam buah eksperimen yang dilakukan secara bertahap. Eksperimen pertama berupa eksperimen menggunakan pustaka HOL. Eksperimen kedua berupa eksperimen memformalisasikan teori gcd yang kemudian memberikan pengetahuan mengenai bentuk formalisasi teori. Eksperimen ketiga menghasilkan struktur data untuk teori graph dan sebuah definisi dari teori graph. Eksperimen keempat menjelaskan beberapa contoh pembuktian menggunakan Taktik yang membantu terbentuknya formalisasi teori graph. Eksperimen kelima dan keenam memaparkan hal-hal yang perlu diperhatikan dari definisi-definisi dan teorema informal dari teori graph. Hasil dari penelitian ini adalah formalisasi dari sebagian teori graph yang dinyatakan dalam 21 definisi penting, 6 definisi umum, 28 definisi bantuan, 3 definisi tanggung, dan 1 teorema. Selain itu, dihasilkan juga pedoman pembuktian menggunakan Taktik dalam sistem HOL. This preliminary research has a goal to produce a formalization of part of graph theory. Graph has been known widely and has many applications. However, a formalization of graph theory has not been implemented in HOL system?s library. This work begins with studying literature about HOL system, then continued with several experiments. There are six experiments. The first experiment is using HOL?s library. The second experiment is formalization on GCD theory, which then elaborates the basic form of formalization. The third experiment produces data structures for graph theory and one definition of graph theory. The fourth experiment describes several proofing examples using Tactic that help make a formalization on graph theory. The fifth and sixth experiments explain things to note from the informal definitions and theorems of graph theory. The result from this research is a formalization of part of graph theory that stated in 21 important definitions, 6 general definitions, 28 helper definitions, 3 pseudo definitions, and 1 theorems. In addition, proofing guidance using Tactic in HOL system also be produced.

Abstrak :
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area.

Abstrak :
Suatu graf sederhana dapat direpresentasikan dalam bentuk matriks Laplacian. Nilai eigen kedua terkecil dari matriks Laplacian, didefinisikan sebagai konektivitas aljabar, memiliki peranan dalam menunjukkan keterhubungan dari graf. Dalam tugas akhir ini, pertama-tama dicari batas atas dari jumlah kuadrat derajat pada suatu graf sederhana. Dari hasil yang diperoleh, kemudian ditentukan batas atas dan bawah dari konektivitas aljabar pada graf. Lebih lanjut dibahas pula batas bawah dari konektivitas aljabar pada graf berbobot.

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A simple graph can be represented by a Laplacian matrix. The second smallest eigenvalue of Laplacian matrix, defined as algebraic connectivity, is used to show the connectivity of graphs. In this skripsi, first we find some upper bounds on the sum of the squares of the degrees in a simple graph. Using these results, we obtain some upper and lower bounds on the algebraic connectivity of graph. In addition, a lower bound on the algebraic connectivity of a weighted graph is also presented.