# Further results on sequentially additive graphs

Suresh Manjanath Hegde; Mirka Miller

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 2, page 251-268
- ISSN: 2083-5892

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topSuresh Manjanath Hegde, and Mirka Miller. "Further results on sequentially additive graphs." Discussiones Mathematicae Graph Theory 27.2 (2007): 251-268. <http://eudml.org/doc/270324>.

@article{SureshManjanathHegde2007,

abstract = {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.},

author = {Suresh Manjanath Hegde, Mirka Miller},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {simply (k-)sequentially additive labelings (graphs); segregated labelings; graph labeling; k-sequentially additive labeling},

language = {eng},

number = {2},

pages = {251-268},

title = {Further results on sequentially additive graphs},

url = {http://eudml.org/doc/270324},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Suresh Manjanath Hegde

AU - Mirka Miller

TI - Further results on sequentially additive graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 2

SP - 251

EP - 268

AB - 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.

LA - eng

KW - simply (k-)sequentially additive labelings (graphs); segregated labelings; graph labeling; k-sequentially additive labeling

UR - http://eudml.org/doc/270324

ER -

## References

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