Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2018, 6(1), 30-33
DOI: 10.12691/tjant-6-1-4
Open AccessArticle

A New Graph Invariant

Sadik Delen1 and Ismail Naci Cangul1,

1Faculty of Arts and Science, Department of Mathematics, Uludag University, 16059 Bursa, Turkey

Pub. Date: March 02, 2018

Cite this paper:
Sadik Delen and Ismail Naci Cangul. A New Graph Invariant. Turkish Journal of Analysis and Number Theory. 2018; 6(1):30-33. doi: 10.12691/tjant-6-1-4

Abstract

The well-known Euler characteristic is an invariant of graphs defined by means of the vertex, edge and face numbers of a graph, to determine the genus of the underlying surface of the graph. By means of it, it is possible to determine the vertex, edge and face numbers of all possible graphs which can be drawn in a given orientable/non-orientable surface. In this paper, by means of a given degree sequence, a new number denoted by which is related to Euler characteristic and has several applications in Graph Theory is defined. This formula gives direct information compared with the Euler characteristic on the realizability, number of realizations, connectedness, being acyclic or cyclic, number of components, chords, loops, pendant edges, faces, bridges etc.

Keywords:
graph characteristic connectedness cyclic graph acyclic graph degree sequence

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References:

[1]  S. L. Hakimi, On the realizability of a set of integers as degrees of the vertices of a graph, J. SIAM Appl. Math., 10 (1962), 496-506.
 
[2]  V. Havel, A remark on the existence of finite graphs (Czech), Časopic Pěst. Mat., 80 (1955), 477-480.