A FEW MORE PROPERTIES OF SUM AND INTEGRAL SUM GRAPHS
نویسندگان
چکیده
منابع مشابه
On integral sum graphs
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 ...
متن کاملRegular integral sum graphs
Given a set of integers S; G(S) = (S; E) is a graph, where the edge uv exists if and only if u+ v∈ S. A graph G = (V; E) is an integral sum graph or ISG if there exists a set S ⊂ Z such that G=G(S). This set is called a labeling of G. The main results of this paper concern regular ISGs. It is proved that all 2-regular graphs with the exception of C4 are integral sum graphs and that for every po...
متن کاملOn integral sum graphs
A graph is said to be a sum graph if there exists a set S of positive integers as its node set, with two nodes adjacent whenever their sum is in S. An integral sum graph is defined just as the sum graph, the difference being that S is a subset of 2~ instead of N*. The sum number of a given graph G is defined as the smallest number of isolated nodes which when added to G result in a sum graph. T...
متن کاملIntegral sum graphs from identification
The idea of integral sum graphs was introduced by Harary (1994). 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 tree is said to be a generalized star if it can be obtained from a star by extending each edge to...
متن کاملOn the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
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ژورنال
عنوان ژورنال: Journal of the Indonesian Mathematical Society
سال: 2014
ISSN: 2460-0245,2086-8952
DOI: 10.22342/jims.20.2.172.148-159