-λ COLORING OF GRAPHS AND CONJECTURE Δ^2

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RAEISI GH.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:2 | Issue:8 Page(s): 59-66

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Information Journal Paper

Title

-λ COLORING OF GRAPHS AND CONJECTURE Δ^2

Author(s)

RAEISI GH. | Issue Writer Certificate

Keywords

λ-COLORINGQ1

Δ^2-CONJECTUREQ1

SQUARED GRAPHQ1

KL-MINOR FREE GRAPHQ1

Abstract

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V (G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G=H2. A function f: V (G) {0, 1, 2…, k} is called a coloring of G if for every pair of vertices x, yV (G) with d (x, y)=1 we have |f (x) -f (y) |2 and also if d (x, y)=2 then |f (x) -f (y) |1. The smallest positive integer k, for which there exists a coloring of G is denoted by. In 1993, Giriggs and Yeh conjectured that for every graph G, with maximum degree. In this paper, we give some upper bounds for coloring of graphs and we confirm this conjecture for SQUARED GRAPHs, line graphs and graphs without minor of K4 and K5.

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APA: Copy

RAEISI, GH.. (2017). -λ COLORING OF GRAPHS AND CONJECTURE Δ^2. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 2(8), 59-66. SID. https://sid.ir/paper/257272/en

Vancouver: Copy

RAEISI GH.. -λ COLORING OF GRAPHS AND CONJECTURE Δ^2. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;2(8):59-66. Available from: https://sid.ir/paper/257272/en

IEEE: Copy

GH. RAEISI, “-λ COLORING OF GRAPHS AND CONJECTURE Δ^2,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 2, no. 8, pp. 59–66, 2017, [Online]. Available: https://sid.ir/paper/257272/en

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