(4, d)-Sigraph and Its Applications
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Let G = (V,E) be a graph. By directional labeling (or d-labeling) of an edge x = uv of G by an ordered 4-tuple (a1, a2, a3, a4), we mean a labeling of the edge x such that we consider the label on uv as (a1, a2, a3, a4) in the direction from u to v, and the label on x as (a4, a3, a2, a1) in the direction from v to u. In this paper, we study graphs, called (4, d)-sigraphs, in which every edge is d-labeled by a 4-tuple (a1, a2, a3, a4), where ak 2 {+, −},for 1 ≤ k ≤ 4. Giving a motivation to study such graphs, we obtain some results by introducing new notions of balance and special types of complementations.
Abstract
Let G = (V,E) be a graph. By directional labeling (or d-labeling) of an edge x = uv of G by an ordered 4-tuple (a1, a2, a3, a4), we mean a labeling of the edge x such that we consider the label on uv as (a1, a2, a3, a4) in the direction from u to v, and the label on x as (a4, a3, a2, a1) in the direction from v to u. In this paper, we study graphs, called (4, d)-sigraphs, in which every edge is d-labeled by a 4-tuple (a1, a2, a3, a4), where ak 2 {+, −},for 1 ≤ k ≤ 4. Giving a motivation to study such graphs, we obtain some results by introducing new notions of balance and special types of complementations.
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