A Multigraph His irregular if no two of its nodeahavethe samedegree.It hasbeen shownthat a graphis the underlying graphof some irregularMultigraph if and only if it has at most one trivialcomponentand no componentsof order2. We definethe irregularity cost of such a graph G to be the minimumnumberof
The irregularity cost or sum of a graph
β Scribed by Frank Harary; Michael S. Jacobson; Ewa Kubicka; Grzegorz Kubicki; Ortrud R. Oellermann
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 169 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
Working simultaneously in two teams [1,2], we have independently discovered essentially the same concept and many common results. As expected, each team used its own notation and terminology but the results are easily transformed between the two systems. We plan to publish our full papers separately, but present the results here.
π SIMILAR VOLUMES
The transmission of a graph or digraph G is the sum of all distances in G. StFict bounds on the transmission are collected and extended for several classes of graphs and digraphs. For example, in the class of 2connected or Z-edge-mnnected graphs of order n, the maximal transmission is realized only
Assign positive integer weights to the edges of a simple graph with no component isomorphic to Ki or 1Β£2, in such a way that the graph becomes irregular, i.e., the weight sums at the vertices become pairwise distinct. The minimum of the largest weights assigned over all such irregular assignments on
Let Ξ» 1 be the largest eigenvalue and Ξ» n the least eigenvalue of the adjacency matrix of a connected graph G of order n. We prove that if G is irregular with diameter D, maximum degree Ξ, minimum degree Ξ΄ and average degree d, then . The inequality improves previous bounds of various authors and