Further results on sequentially additive graphs

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

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Abstract

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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.

How to cite

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Suresh 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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7. [7] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combinatorics DS#6 (2003) 1-148.
8. [8] S.W. Golomb, How to number a graph, in: Graph Theory and Computing, (ed. R.C. Read) (Academic Press, 1972), 23-37. Zbl0293.05150
10. [10] S.M. Hegde, On indexable graphs, J. Combin., Information & System Sciences 17 (1992) 316-331. Zbl1231.05229
11. [11] S.M. Hegde and Shetty Sudhakar, Strongly k-indexable labelings and super edge magic labelings are equivalent, NITK Research Bulletin 12 (2003) 23-28.
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