5 research outputs found
p-νκ·Έλνμ p-κ²½μκ·Έλν
νμλ
Όλ¬Έ (μμ¬)-- μμΈλνκ΅ λνμ : μ¬λ²λν μνκ΅μ‘κ³Ό, 2019. 2. κΉμλ Ή.For a positive integer , the -competition graph of a digraph is a graph which has the same vertex set as and an edge between distinct vertices and if and only if and have at least common out-neighbors in . A graph is said to be a -competition graph if it is the -competition graph of a digraph. In this paper, we introduce { the notions of -row graph of a matrix and competition-realizer for a graph} to study -competition graphs. {Using these notions}, we study the competition-realizers of various graphs to extend results given by Kim {\it et al.}~[-competition graphs,
{\it Linear Algebra Appl.} {\bf 217} (1995) 167--178]. Especially, we completely characterize the competition-realizers for caterpillars.μμ μ μ μ λν΄, μ΄λ€ μ ν₯κ·Έλν μ -κ²½μκ·Έλνλ κΌμ§μ μ μ§ν©μ μ κ°μ΄ κ°κ³ λ κΌμ§μ μ κ° λ³μΌλ‘ μ΄μ΄μ§ νμμΆ©λΆμ‘°κ±΄μ μ κ° μ΅μν κ° μ΄μμ 곡ν΅λ μΈμ΄μμ κ°μ§λ κ²μΌλ‘ νλ κ·Έλνλ‘ μ μλλ€. μ΄λ€ κ·Έλν μ λν΄ μ΄λ€ μ ν₯κ·Έλν κ° μ‘΄μ¬ν΄μ κ° μ -κ²½μκ·Έλνκ° λ λ λ₯Ό -κ²½μκ·ΈλνλΌκ³ λΆλ₯Έλ€. κ·Έλν κ° μ£Όμ΄μ‘μ λ, κ° -κ²½μκ·Έλνκ° λλ μμ μ μ μ μ§ν©μ μ κ²½μμ€νμ§ν©μ΄λΌκ³ μ μνλ€. κ·Έλν μ λν΄μ μλ‘ κ°μ λ«ν μΈμ΄μμ κ°λ μΈμ ν κΌμ§μ μ λμΌμνμ¬ μ»μ κ·Έλνλ₯Ό μΌλ‘ λνλΈλ€. λ³Έ μ°κ΅¬μμλ κΈ°μ‘΄μ νκ·Έλνμ λν κ°λ
μ νμ₯ν -νκ·Έλνλ₯Ό λμ
νμκ³ , -νκ·Έλνμ μ μ΄μ©νμ¬ λ€μν κ·Έλνμ κ²½μμ€νμ§ν©μ μ°Ύμλ΄μμΌλ©° κΈ°μ‘΄μ μ°κ΅¬μμ λμλ κ²°κ³Όλ€μ νμ₯νμμΌλ©° μνλμ μΌμ’
μΈ μΊν°νλ¬μ κ²½μμ€νμ§ν©μ λͺ¨λ μμλ₯Ό μ°Ύμλ΄μλ€.1. Introduction
2. -row graphs and competition-realizers
3. Competition-realizers for trees
4. Closing RemarksMaste