Article citationsMore >>

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.

has been cited by the following article:

Article

A New Graph Invariant

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


Turkish Journal of Analysis and Number Theory. 2018, Vol. 6 No. 1, 30-33
DOI: 10.12691/tjant-6-1-4
Copyright © 2018 Science and Education Publishing

Cite this paper:
Sadik Delen, 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.

Correspondence to: Ismail  Naci Cangul, Faculty of Arts and Science, Department of Mathematics, Uludag University, 16059 Bursa, Turkey. Email: ncangul@gmail.com

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