The Irregularity and Total Irregularity of Eulerian Graphs

نویسندگان
Ellahi, H. R. ID 1
Gholami, A. ID 2
Fath-Tabar, G. H. ID 3
Nasiri, R. ID 4

1 Department of Mathematics, University of Qom, Qom, I. R. Iran

2 Department of Mathematics, University of Qom, Qom, I. R. Iran

3 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran

4 Department of Mathematics, University of Qom, Qom, I. R. Iran

doi
10.22052/ijmc.2018.44232.1153
چکیده

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

کلیدواژه‌ها
Eulerian graphs, irregularity, total irregularity, vertex degree