Combinatorics, Graph Theory and Computing: SEICCGTC 2020, Boca Raton, USA, March 9–13

Preface I
Preface II
Contents
Ratio Balancing Numbers
	1 Introduction
	2 Ratio Balancing Numbers and Related Quantities
	3 Counting Ratio Balancing Numbers
	4 Functions Generating Ratio Balancing Numbers and Related Results
		4.1 One Jump Case
		4.2 Two Jump Case
	References
An Unexpected Digit Permutation from Multiplying in Any Number Base
	1 Introduction
	2 Main Theorem
	3 Other Interesting Results
	4 Demonstration of Results
	5 Questions for Further Investigation
	References
A & Z Sequences for Double Riordan Arrays
	1 Introduction
	2 Double Riordan: A & Z Sequences
	3 New Subgroups
	4 Conclusion
	References
Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs; A New Proof of the Friendship Theorem
	1 Introduction
	2 Preliminaries for a Clifford Graph Algebra
	3 Clifford Algebras for Windmill and Dutch Windmill Graphs
		3.1 Windmill Graphs
		3.2 Dutch Windmill Graphs
		3.3 The Friendship Graph
		3.4 The Clifford Algebra for the Friendship Graph
		3.5 The Clifford Algebra for the Class of Windmill Graphs
		3.6 The Clifford Algebra for the Class of Dutch Windmill Graphs
	4 The Friendship Theorem
		4.1 Standard Preliminaries for the Friendship Theorem
		4.2 Clifford Algebra Preliminaries for the Friendship Theorem
		4.3 Proof of the Friendship Theorem
	5 Concluding Remarks
	References
Finding Exact Values of a Character Sum
	1 Introduction
	2 Proofs
	3 Counting Points on left parenthesis asterisk asterisk asterisk right parenthesis(***)
	4 Examples
	5 Conclusion
	References
On Minimum Index Stanton 44-Cycle Designs
	1 Introduction
	2 Stanton 4-Cycles
	3 Small Decompositions
	4 Decompositions via Graph Labellings
	5 Main Result
	References
kk-Plane Matroids and Whiteley\'s Flattening Conjectures
	1 kk-Plane Matroids
	2 The 22-Plane Matroid and the Connectivity of the Incidence Graph
	3 Connection to 2-d Rigidity
	References
Bounding the Trace Function of a Hypergraph with Applications
	1 Introduction and Summary
	2 Main Results
	3 Applications to VC Dimension
	4 Applications to Domination Theory
	References
A Generalization on Neighborhood Representatives
	References
Harmonious Labelings of Disconnected Graphs Involving Cycles and Multiple Components Consisting of Starlike Trees
	1 Introduction
	2 Main Results
	References
On Rainbow Mean Colorings of Trees
	1 Introduction
	2 Rainbow Mean Colorings
	3 The Rainbow Mean Index of Trees
	4 Cubic Caterpillars
	5  Subdivided Stars
	6 Double Stars
	References
Examples of Edge Critical Graphs in Peg Solitaire
	1 Introduction
	2 The Hairy Complete Bipartite Graph
	3 Edge Critical Results
	4 Graphs on Eight Vertices
	References
Regular Tournaments with Minimum Split Domination Number and Cycle Extendability
	1 The Lower Bound
	2 Properties of Tournaments That Meet the Bound
	References
Independence and Domination of Chess Pieces on Triangular Boards and on the Surface of a Tetrahedron
	1 Introduction
	2 Triangular Boards with Triangular Spaces
		2.1 Independence on upper T Subscript nTn
		2.2 Domination on upper T Subscript nTn
	3 Triangular Boards with Hexagonal Spaces
		3.1 Independence on upper H Subscript nHn
		3.2 Domination on upper H Subscript nHn
	4 Triangular Boards on the Surface of a Tetrahedron
		4.1 Independence and Domination on upper T Superscript nTn
		4.2 Independence and Domination on upper H Superscript nHn
	References
Efficient and Non-efficient Domination of double struck upper ZmathbbZ-stacked Archimedean Lattices
	1 Introduction
		1.1 Efficient Domination
		1.2 double struck upper ZmathbbZ-stacked Archimedean Lattices
		1.3 Domination Ratio and Periodic Graph
		1.4 Overview of Results
	2 Proving Efficient Domination
		2.1 Simplification of Criteria for Efficient Domination
		2.2 Additional Conditions
	3 Efficiently Dominated Lattices
		3.1 left parenthesis 4 Superscript 4 Baseline right parenthesis times double struck upper Z(44)timesmathbbZ Lattice and double struck upper Z Superscript nmathbbZn
		3.2 left parenthesis 3 Superscript 6 Baseline right parenthesis times double struck upper Z(36)timesmathbbZ Lattice
		3.3 left parenthesis 6 cubed right parenthesis times double struck upper Z(63)timesmathbbZ Lattice
		3.4 left parenthesis 4 comma 8 squared right parenthesis times double struck upper Z(4,82)timesmathbbZ Lattice
		3.5 left parenthesis 4 comma 6 comma 12 right parenthesis times double struck upper Z(4,6,12)timesmathbbZ Lattice
		3.6 left parenthesis 3 squared comma 4 comma 3 comma 4 right parenthesis times double struck upper Z(32,4,3,4)timesmathbbZ Lattice
		3.7 left parenthesis 3 cubed comma 4 squared right parenthesis times double struck upper Z(33,42)timesmathbbZ Lattice
	4 Non-efficiently-dominatable double struck upper ZmathbbZ-stacked Archimedean Lattices
	5 Future Research
	References
On Subdivision Graphs Which Are 22-steps Hamiltonian Graphs and Hereditary Non 22-steps Hamiltonian Graphs
	1 Introduction
	2 Subdivision Graphs of a Wheel Graph
	3 Subdivision Graphs of upper C 4 times upper K 2C4 timesK2 on Its Perfect Matching
	References
On the Erdős-Sós Conjecture for Graphs with Circumference at Most k plus 1k+1
	1 Introduction
	2 Supporting Lemmas
	3 Proof of the Main Theorem
	References
Regular Graph and Some Vertex-Deleted Subgraph
	1 Introduction
	2 Prepare for Proofs
		2.1 Proof of Theorem 3
	3 Proof of Theorem 2
	4 Proof of Remark 1 and Theorem 1
	5 Sharpness
	References
Connectivity and Extendability in Digraphs
	1 Introduction
	2 Preliminaries
	3 Connectivity
		3.1 Examples and Containment
	4 Extendability
		4.1 Definitions—Path- and Cycle-Extendability
		4.2 Definitions—Sets of Graphs Defined by Extendability
		4.3 Examples and Containment
		4.4 Summary
	5 Set Connectivity and Extendability
		5.1 Definitions—upper SS-Path- and upper SS-Cycle-Extendability
		5.2 Sets Defined by Set-Continuity and Set-Extendability
	References
On the Extraconnectivity of Arrangement Graphs
	1 Introduction
	2 StartSet 4 comma 5 comma 6 EndSet{4,5,6}-Extraconnectivities
	References
kk-Paths of kk-Trees
	1 Introduction
	2 Diameter of kk-Trees
	References
Rearrangements of the Simple Random Walk
	1 Introduction
	2 Representation Results
	3 Rearrangements of the Random Walk
	4 Graph-Theoretic Complexity of the Permutations
	References
On the Energy of Transposition Graphs
	1 Introduction
		1.1 Definitions
		1.2 Symmetry and Recursive Scalability
	2 Transposition Graphs
	3 Energy and Spectra of Graphs
		3.1 Energy of Graphs
		3.2 Spectra of script upper TmathcalT
	4 Bounds on the Energy of Transposition Graphs
	References
A Smaller Upper Bound for the left parenthesis 4 comma 8 squared right parenthesis(4,82) Lattice Site Percolation Threshold
	1 Introduction
	2 Bounds for the left parenthesis 4 comma 8 squared right parenthesis(4,82) Lattice Site Percolation Threshold
	3 Derivation of the Upper Bound
		3.1 Substitution Method
		3.2 Substitution Regions
		3.3 The Comparison Lattice
		3.4 Set Partitions of the Boundary Vertices
		3.5 The Partition Lattice and Stochastic Ordering
		3.6 ``Finding Two Needles in a Haystack\'\'
		3.7 Non-crossing Partitions
		3.8 Symmetry Reduction
		3.9 Network Flow Model
	4 Future Research
	References