### Abstract

A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some node w in G. A node of G is called a saturated node if it is adjacent to every other node of G. We show that any integral sum graph which is not K_{3} has at most two saturated nodes. We determine the structure for all integral sum graphs with exactly two saturated nodes, and give an upper bound for the number of edges of a connected integral sum graph with no saturated nodes. We introduce a method of identification on constructing new connected integral sum graphs from given integral sum graphs with a saturated node. Moreover, we show that every graph is an induced subgraph of a connected integral sum graph. Miscellaneous relative results are also presented.

Original language | English (US) |
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Pages (from-to) | 117-127 |

Number of pages | 11 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 11 |

DOIs | |

State | Published - Jul 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*11*, 117-127. https://doi.org/10.1016/S1571-0653(04)00060-5

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*Electronic Notes in Discrete Mathematics*, vol. 11, pp. 117-127. https://doi.org/10.1016/S1571-0653(04)00060-5

**On Integral Sum Graphs.** / Chen, Zhibo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Integral Sum Graphs

AU - Chen, Zhibo

PY - 2002/7/1

Y1 - 2002/7/1

N2 - A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some node w in G. A node of G is called a saturated node if it is adjacent to every other node of G. We show that any integral sum graph which is not K3 has at most two saturated nodes. We determine the structure for all integral sum graphs with exactly two saturated nodes, and give an upper bound for the number of edges of a connected integral sum graph with no saturated nodes. We introduce a method of identification on constructing new connected integral sum graphs from given integral sum graphs with a saturated node. Moreover, we show that every graph is an induced subgraph of a connected integral sum graph. Miscellaneous relative results are also presented.

AB - A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some node w in G. A node of G is called a saturated node if it is adjacent to every other node of G. We show that any integral sum graph which is not K3 has at most two saturated nodes. We determine the structure for all integral sum graphs with exactly two saturated nodes, and give an upper bound for the number of edges of a connected integral sum graph with no saturated nodes. We introduce a method of identification on constructing new connected integral sum graphs from given integral sum graphs with a saturated node. Moreover, we show that every graph is an induced subgraph of a connected integral sum graph. Miscellaneous relative results are also presented.

UR - http://www.scopus.com/inward/record.url?scp=34247092553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247092553&partnerID=8YFLogxK

U2 - 10.1016/S1571-0653(04)00060-5

DO - 10.1016/S1571-0653(04)00060-5

M3 - Article

AN - SCOPUS:34247092553

VL - 11

SP - 117

EP - 127

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -