The characteristic polynomial of a graph containing loops

In this article, we focus on the characteristic polynomial of a graph containing loops without multiple edges. We present a relationship between the characteristic polynomial of a graph containing loops without multiple edges and the graph obtained by removing all the loops. In turn, we compute the characteristic polynomial of unitary addition Cayley graphs. 2010 Mathematics Subject Classifications: 05C50.

[1]  D. Bonchev.  Chemical Graph Theory: Introduction and Fundamentals , 1991 .

[2]  Jerry Ray Dias,et al.  Chemical Applications of Graph Theory , 1992 .

[3]  E. V. Babaev,et al.  The Concepts of Periodicity and Hyperperiodicity : from Atoms to Molecules , 2011 .

[4]  Leonard Spialter.  The Atom Connectivity Matrix (ACM) and Its Characteristic Polynomial (ACMCP). , 1964 .

[5]  B. Devadas Acharya,et al.  Spectral criterion for cycle balance in networks , 1980, J. Graph Theory.

[6]  James Dugundji,et al.  An algebraic model of constitutional chemistry as a basis for chemical computer programs , 1973 .

[7]  F. Harary.  On the notion of balance of a signed graph. , 1953 .

[8]  James A. Davis.  Clustering and Structural Balance in Graphs , 1977 .

[9]  Irving Langmuir,et al.  THE ARRANGEMENT OF ELECTRONS IN ATOMS AND MOLECULES. , 1919 .

[10]  J. W. COOK,et al.  Molecular Geometry , 1960, Nature.

[11]  Associazione per la matematica applicata alle scienze economich sociali.  Rivista di matematica per le scienze economiche e sociali , 1978 .

[12]  István Hargittai,et al.  The Vsepr Model of Molecular Geometry , 1991 .

[13]  William B. Jensen,et al.  The Lewis Acid-Base Concepts: An Overview , 1979 .

[14]  Deepa Sinha,et al.  Some properties of unitary addition Cayley graphs , 2012 .

[15]  A. Schwenk.  COMPUTING THE CHARACTERISTIC POLYNOMIAL OF A GRAPH. , 1974 .

[16]  Gilbert N. Lewis,et al.  Valence And The Structure Of Atoms And Molecules , 1923 .

[17]  Frank Harary,et al.  Consistent graphs with signed points , 1978 .