Titlebook: Combinatorics, Graph Theory and Computing; SEICCGTC 2021, Boca Frederick Hoffman,Sarah Holliday,John Wierman Conference proceedings 2024 T

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钢笔尖

opinionated

,Graph Constructions Derived from Interconnection Networks,er. For Dragonfly networks, the building block network is a complete graph and the wiring together is done by either a cycle or a complete graph. The process may be viewed as a way to construct a new graph from two component graphs.The resulting graph is known as a replacement graph. Furthermore, on

Admonish

,On the Target Pebbling Conjecture,ansit. The pebbling number of a demand in a graph is the smallest number for which every placement of that many supply pebbles satisfies the demand. The Target Conjecture (Herscovici-Hester-Hurlbert, 2009) posits that the largest pebbling number of a demand of fixed size . occurs when the demand is

Fibrinogen

DECRY

,On the Locating Rainbow Connection Number of the Comb Product with Complete Graphs or Trees, and define the locating rainbow connection number within this framework. Our main results establish tight upper and lower bounds for . in the context of comb products. Additionally, we determine the locating rainbow connection number for the comb product of an arbitrary graph with a complete graph

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Urgency

,The ,-splitting Operation for Matroids Representable Over Prime Fields ,(,),onnectivity of the .-matoids. A Sufficient condition to obtain a 3-connected .-matroid from a 3-connected .-matroid using the .-splitting operation is also provided. In the last section, we obtain a sufficient condition to produce an Eulerian .-matroid from an Eulerian .-matroid using .-splitting operation.

hedonic

Differences of Functions with the Same Value Multiset,ger version of Hall’s theorem, which gives a description of . and . in terms of .. We conclude by presenting further directions and questions that relate this new approach to applications of Hall’s theorem.

CAMEO

,Nonexistence of a Subfamily of a Family of Edge-Regular Graphs,tions, where . is the number of vertices and .. We consider the case where ., with the added condition that the common neighbor set of every pair of adjacent vertices induces ., a disjoint union of edges.