ON LAPLACIAN EIGENVALUES OF GRAPHS

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DAS KINKAR CH.

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Seminar Paper

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Seminar: ANNUAL IRANIAN MATHEMATICS CONFERENCE
Year:2015 | Issue:46

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Title

ON LAPLACIAN EIGENVALUES OF GRAPHS

Author(s)

DAS KINKAR CH. | Issue Writer Certificate

Keywords

GRAPH

LARGEST LAPLACIAN EIGENVALUE

ALGEBRAIC CONNECTIVITY

DIAMETER

MINIMUM DEGREE

Abstract

LET G= (V, E) BE A SIMPLE GRAPH. DENOTE BY D (G) THE DIAGONAL MATRIX OF ITS VERTEX DEGREES AND BY A (G) ITS ADJACENCY MATRIX. THEN THE LAPLACIAN MATRIX OF G IS L(G) =D (G) − A (G). DENOTE THE SPECTRUM OF L (G) BY S (L (G)) = (M1, M2, ..., MN), WHERE WE ASSUME THE EIGENVALUES TO BE ARRANGED IN NON-INCREASING ORDER: M1 ³ M2 ³ · · · MN-1 ³ MN=0. LET A BE THE ALGEBRAIC CONNECTIVITY OF GRAPH G. THEN A= MN-1.AMONG ALL EIGENVALUES OF THE LAPLACIAN MATRIX OF A GRAPH, THE MOST STUDIED IS THE SECOND SMALLEST, CALLED THE ALGEBRAIC CONNECTIVITY (A (G)) OF A GRAPH [5]. IN THIS TALK WE SHOW SOME RESULTS ON M1(G) AND A (G) OF GRAPH G. WE OBTAIN SOME INTEGER AND REAL LAPLACIAN EIGENVALUES OF GRAPHS. MOREOVER, WE DISCUSS SEVERAL RELATIONS BETWEEN LAPLACIAN EIGENVALUES AND GRAPH PARAMETERS. FINALLY, WE GIVE SOME CONJECTURES ON THE LAPLACIAN EIGENVALUES OF GRAPHS.

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APA: Copy

DAS, KINKAR CH.. (2015). ON LAPLACIAN EIGENVALUES OF GRAPHS. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/920913/en

Vancouver: Copy

DAS KINKAR CH.. ON LAPLACIAN EIGENVALUES OF GRAPHS. 2015. Available from: https://sid.ir/paper/920913/en

IEEE: Copy

KINKAR CH. DAS, “ON LAPLACIAN EIGENVALUES OF GRAPHS,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2015, [Online]. Available: https://sid.ir/paper/920913/en

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