Geodesic
Further results on sequentially additive graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 251-268

Voir la notice de l'article provenant de la source Library of Science

Given a graph G with p vertices, q edges and a positive integer k, a k-sequentially additive labeling of G is an assignment of distinct numbers k,k+1,k+2,...,k+p+q-1 to the p+q elements of G so that every edge uv of G receives the sum of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its elements is called a k-sequentially additive graph. In this paper, we give an upper bound for k with respect to which the given graph may possibly be k-sequentially additive using the independence number of the graph. Also, we prove a variety of results on k-sequentially additive graphs, including the number of isolated vertices to be added to a complete graph with four or more vertices to be simply sequentially additive and a construction of an infinite family of k-sequentially additive graphs from a given k-sequentially additive graph.
Keywords: simply (k-)sequentially additive labelings (graphs), segregated labelings 
@article{DMGT_2007_27_2_a3,
     author = {Hegde, Suresh and Miller, Mirka},
     title = {Further results on sequentially additive graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {251--268},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a3/}
}
TY  - JOUR
AU  - Hegde, Suresh
AU  - Miller, Mirka
TI  - Further results on sequentially additive graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 251
EP  - 268
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a3/
LA  - en
ID  - DMGT_2007_27_2_a3
ER  - 
%0 Journal Article
%A Hegde, Suresh
%A Miller, Mirka
%T Further results on sequentially additive graphs
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 251-268
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a3/
%G en
%F DMGT_2007_27_2_a3
Hegde, Suresh; Miller, Mirka. Further results on sequentially additive graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 251-268. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a3/