# On Integral Sum Graphs

Zhibo Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 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.

Original language English (US) 117-127 11 Electronic Notes in Discrete Mathematics 11 https://doi.org/10.1016/S1571-0653(04)00060-5 Published - Jul 1 2002

### Fingerprint

Labeling
Graph in graph theory
Vertex of a graph
Distinct
Induced Subgraph
Upper bound
If and only if
Integer

### All Science Journal Classification (ASJC) codes

• Discrete Mathematics and Combinatorics
• Applied Mathematics

### Cite this

Chen, Zhibo. / On Integral Sum Graphs. In: Electronic Notes in Discrete Mathematics. 2002 ; Vol. 11. pp. 117-127.
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On Integral Sum Graphs. / Chen, Zhibo.

In: Electronic Notes in Discrete Mathematics, Vol. 11, 01.07.2002, p. 117-127.

Research output: Contribution to journalArticle

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