Fundamental Concepts Graphs and Simple Graphs Matrices and Isomorphisms Paths and Cycles Vertex Degrees Graph Operations Some Basic Techniques Degree Sequences Applications on Graph Isomorphisms Generalized Honeycomb Tori Isomorphism between Cyclic-Cubes and Wrapped Butterfly Networks 1-Edge Fault-Tolerant Design for Meshes Faithful 1-Edge Fault-Tolerant Graphs k-Edge Fault-Tolerant Designs for Hypercubes Distance and Diameter Diameter for Some Interconnection Networks Shuffle-Cubes Moore Bound Star Graphs and Pancake Graphs Edge Congestion and Bisection Width Transmitting Problem Trees Basic Properties Breadth-First Search and Depth-First Search Rooted Trees Counting Trees Counting Binary Trees Number of Spanning Trees Contains a Certain Edge Embedding Problem Eulerian Graphs and Digraphs Eulerian Graphs Eulerian Digraphs Applications Matchings and Factors Matchings Bipartite Matching Edge Cover Perfect Matching Factors Connectivity Cut and Connectivity 2-Connected Graphs Menger Theorem An Application--Making a Road System One-Way Connectivity of Some Interconnection Networks Wide Diameters and Fault Diameters Superconnectivity and Super-Edge-Connectivity Graph Coloring Vertex Colorings and Bounds Properties of k-Critical Graphs Bound for Chromatic Numbers Girth and Chromatic Number Hajós'' Conjecture Enumerative Aspects Homomorphism Functions An Application--Testing on Printed Circuit Boards Edge-Colorings Hamiltonian Cycles Hamiltonian Graphs Necessary Conditions Sufficient Conditions Hamiltonian-Connected Mutually Independent Hamiltonian Paths Diameter for Generalized Shuffle-Cubes Cycles in Directed Graphs Planar Graphs Planar Embeddings Euler''s Formula Characterization of Planar Graphs Coloring of Planar Graphs Optimal k-Fault-Tolerant Hamiltonian Graphs Node Expansion Other Construction Methods Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the Folded Petersen Cube Networks Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the Pancake Graphs Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of Augmented Cubes Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the WK-Recursive Networks Fault-Tolerant Hamiltonicity of the Fully Connected Cubic Networks Optimal 1-Fault-Tolerant Hamiltonian Graphs 3-Join Cycle Extension Cells for Optimal 1-Hamiltonian Regular Graphs Generalized Petersen Graphs Honeycomb Rectangular Disks Properties with Respect to the 3-Join Examples of Various Cubic Planar Hamiltonian Graphs Hamiltonian Properties of Double Loop Networks Optimal k-Fault-Tolerant Hamiltonian-Laceable Graphs Super Fault-Tolerant Hamiltonian Laceability of Hypercubes Super Fault-Tolerant Hamiltonian Laceability of Star Graphs Construction Schemes Cubic Hamiltonian-Laceable Graphs 1p-Fault-Tolerant Hamiltonian Graphs Hamiltonian Laceability of Faulty Hypercubes Conditional Fault Hamiltonicity and Conditional Fault Hamiltonian Laceability of the Star Graphs Spanning Connectivity Spanning Connectivity of General Graphs Spanning Connectivity and Spanning Laceability of the Hypercube-Like Networks Spanning Connectivity of Crossed Cubes Spanning Connectivity and Spanning Laceability of the Enhanced Hypercube Networks Spanning Connectivity of the Pancake Graphs Spanning Laceability of the Star Graphs Spanning Fan-Connectivity and Spanning Pipe-Connectivity of Graphs Cubic 3*-Connected Graphs and Cubic 3*-Laceable Graphs Properties of Cubic 3*-Connected Graphs Examples of Cubic Super 3*-Connected Graphs Counterexamples of 3*-Connected Graphs Properties of Cubic 3*-Laceable Graphs Examples of Cubic Hyper 3*-Laceable Graphs Counterexamples of 3*-Laceable Graphs Spanning Diameter Spanning Diameter for the Star Graphs Spanning Diameter of Hypercubes Spanning Diameter for Some (n, k)-Star Graphs Pancyclic and Panconnected Property Bipanconnected and Bipancyclic Properties of Hypercubes Edge Fault-Tolerant Bipancyclic Properties of Hypercubes Panconnected and Pancyclic Properties of Augmented Cubes Comparison between Panconnected and Panpositionable Hamiltonian Bipanpositionable Bipancyclic Property of Hypercube Mutually Independent Hamiltonian Cycles Mutually Independent Hamiltonian Cycles on Some Graphs Mutually Independent Hamiltonian Cycles of Hypercubes Mutually Independent Hamiltonian Cycles of Pancake Graphs Mutually Independent Hamiltonian Cycles of Star Graphs Fault-Free Mutually Independent Hamiltonian Cycles in a Faulty Hypercube Fault-Free Mutually Independent Hamiltonian Cycles in Faulty Star Graphs Orthogonality for Sets of Mutually Independent Hamiltonian Cycles &l> Moore Bound Star Graphs and Pancake Graphs Edge Congestion and Bisection Width Transmitting Problem Trees Basic Properties Breadth-First Search and Depth-First Search Rooted Trees Counting Trees Counting Binary Trees Number of Spanning Trees Contains a Certain Edge Embedding Problem Eulerian Graphs and Digraphs Eulerian Graphs Eulerian Digraphs Applications Matchings and Factors Matchings Bipartite Matching Edge Cover Perfect Matching Factors Connectivity Cut and Connectivity 2-Connected Graphs Menger Theorem An Application--Making a Road System One-Way Connectivity of Some Interconnection Networks Wide Diameters and Fault Diameters Superconnectivity and Super-Edge-Connectivity Graph Coloring Vertex Colorings and Bounds Properties of k-Critical Graphs Bound for Chromatic Numbers Girth and Chromatic Number Hajós'' Conjecture Enumerative Aspects Homomorphism Functions An Application--Testing on Printed Circuit Boards Edge-Colorings Hamiltonian Cycles Hamiltonian Graphs Necessary Conditions Sufficient Conditions Hamiltonian-Connected Mutually Independent Hamiltonian Paths Diameter for Generalized Shuffle-Cubes Cycles in Directed Graphs Planar Graphs Planar Embeddings Euler''s Formula Characterization of Planar Graphs Coloring of Planar Graphs Optimal k-Fault-Tolerant Hamiltonian Graphs Node Expansion Other Construction Methods Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the Folded Petersen Cube Networks Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the Pancake Graphs Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of Augmented Cubes Fault-Tolerant Hamiltonicity and Fault-Tolerant Hamiltonian Connectivity of the WK-Recursive Networks Fault-Tolerant Hamiltonicity of the Fully Connected Cubic Networks Optimal 1-Fault-Tolerant Hamiltonian Graphs 3-Join Cycle Extension Cells for Optimal 1-Hamiltonian Regular Graphs Generalized Petersen Graphs Honeycomb Rectangular Disks Properties with Respect to the 3-Join Examples of Various Cubic Planar Hamiltonian Graphs Hamiltonian Properties of Double Loop Networks Optimal k-Fault-Tolerant Hamiltonian-Laceable Graphs Super Fault-Tolerant Hamiltonian Laceability of Hypercubes Super Fault-Tolerant Hamiltonian Laceability of Star Graphs Construction Schemes Cubic Hamiltonian-Laceable Graphs 1p-Fault-Tolerant Hamiltonian Graphs Hamiltonian Laceability of Faulty Hypercubes Conditional Fault Hamiltonicity and Conditional Fault Hamiltonian Laceability of the Star Graphs Spanning Connectivity Spanning Connectivity of General Graphs Spanning Connectivity and Spanning Laceability of the Hypercube-Like Networks Spanning Connectivity of Crossed Cubes Spanning Connectivity and Spanning Laceability of the Enhanced Hypercube Networks Spanning Connectivity of the Pancake Graphs Spanning Laceability of the Star Graphs Spanning Fan-Connectivity and Spanning Pipe-Connectivity of Graphs Cubic 3*-Connected Graphs and Cubic 3*-Laceable Graphs Properties of Cubic 3*-Connected Graphs Examples of Cubic Super 3*-Connected Graphs Counterexamples of 3*-Connected Graphs Properties of Cubic 3*-Laceable Graphs Examples of Cubic Hyper 3*-Laceable Graphs Counterexamples of 3*-Laceable Graphs Spanning Diameter Spanning Diameter for the Star Graphs Spanning Diameter of Hypercubes Spanning Diameter for Some (.