Algebraic Analysis of Vertex-Distinguishing Edge-Colorings

Mathematics;algebraic graph theory;graph coloring;edge coloring;edge-coloring;vertex distinguishing;vertex-distinguishing;vdec

Clark, David

University of Waterloo

关键词: Mathematics;    algebraic graph theory;    graph coloring;    edge coloring;    edge-coloring;    vertex distinguishing;    vertex-distinguishing;    vdec;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1053/1/d3clark2006.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.